I have two of these, both with fabric bodies and painted eyes. I got them on the secondary market, so I'm making the assumption that all the bits are original but I don't know that for sure.
Here they are, along with the Mini Molly that's Courtney's Pleasant Company Doll.
The first Mini Molly that I have came in the burgundy box with The American Girls Collection branding and the "Celebrating Girls of Yesterday" banner underneath the oval cellophane window. The side of the box pictures seven American Girls (Felicity, Josefina, Kirsten, Addy, Samantha, Kit, and Molly), so this version dates to around 2000-2002 (after Kit joined the lineup in 2000, and before Kaya joined in 2002.)
Molly's body is made of soft fabric and her head and limbs are vinyl. Unlike the other versions I have, her limbs don't move very well. Maybe she's a bit stiff from sitting in her box for so long. She has rooted brown hair, painted grey eyes, and painted eyelashes on the top. Her long brown braids with the red bows at the end hang pretty straight but her bangs poof up, like others mentioned.
She has neck strings and her body has an American Girl label on the side, but if you look carefully, you can see a faint "2000 Pleasant Company" imprint on the back of her neck, in all capital letters.
A dark thread in the fabric near her neck makes me wonder if her clothes were sewn on at one time; however, they are removable. The little sweater looks like her regular meet sweater with its blue sleeves, blue back, and blue and red argyle design with green accent threads in the front. It's not quite proportionally scaled down, and the seams make the whole thing seem bulky on her, but I'm not sure if there's a better way to do it. As others have mentioned, her white collar with embroidered zigzag design is sewn to the neckline of the sweater and is not a separate piece. This version is sewn partway up in the back, and then has two snaps that can be opened to remove the sweater from the doll. (It's a snug fit over her head, though, and I suspect that taking the sweater off several times would likely result in pulling the braids a little looser so they'd eventually curl up - Although I have no idea if that's what caused the curling up other posters reported.)
The dark blue wool(?) skirt attaches with a bit of Velcro in the back. It also has an American Girl label sewn in the seam inside (none of the other pieces of the outfit do). The outfit also comes with white bloomers, white socks, black shoes, and thin plastic silver-colored glasses (they've got round frames and the round part over the nose, with straight arms).
The book that this Mini Molly came with is a hardcover parchment colored edition of Meet Molly Book 1. The pages have words and illustrations but it's not the complete first book inside. The back cover shows the six-book series, and the copyright page says 2001, so I guess that might narrow this doll down to 2001-2002.
The other Mini Molly that I have is similar in many ways (fabric body, rooted brown hair, painted eyes, same type of outfit), so I'll try to highlight the differences.
Her packaging is in a bright red "American Girl"-branded box with the big cellophane window that shows the whole Mini Molly. The back of this package has a 2015 copyright. Mini dolls started getting all-vinyl bodies in 2014, but I think the Mini Molly dolls were still getting fabric bodies after that.
Like the earlier Mini Molly, this one has a neck strings and a fabric body. This one has a '©American Girl" lightly imprinted on the back of the neck, and she has two body tags, one that says American Girl and the other with some sort of code (looks like 1410NF). Her limbs all move with greater ease and she is much more pliable than her older counterpart. Her bangs lay flatter, and I think she has a bit more face color as well.
Her clothes are generally pretty similar, with only minor difference. The sweater has a Velcro closure instead of snaps, the collar lays flatter, and in general it seems like the sweater and the seams are a little less bulky. I think it's an improvement both in terms of how it looks on Molly, and the ease with which you can take it on/off if you want to. There's a little label sewn into the seam of this sweater (with just a code, 0680BKG). The skirt has two labels, one American Girl label and the other a code that matches the doll's body tag (1410NF). The back of the American Girl label has washing instructions to hand wash and line dry. I didn't look at the socks, shoes, or bloomers in detail but they appear to be similar, and I didn't get glasses with this Molly on the secondary market.
Sweaters, side by side, from the back:
The book that this one came with is the blue hardcover Meet Molly that shows her in her Hula Halloween Costume. Like the earlier version, this shows the six-book series on the back and has writing and illustrations inside from two chapters of the actual book. (For some reason, they chose to include Chapter 1 Turnips and Chapter 4 War, but have numbered the pages as if these come sequentially.) This isn't the BeForever-branded book that would have come out in 2014, so I'm guessing this Mini Molly set dates from somewhere between 2004 (when the Meet Book changed to the Halloween Costume) and 2014 (when the cover of the girl-sized books changed again to reflect the BeForever branding). The inside of the book still has the 2001 copyright date.
Overall, I think both of these fabric-bodied dolls are pretty detailed and have some good qualities, most especially the smaller scale. I think either of these versions are good options for people who want dolls for their dolls or who just want to create a smaller scale doll world.
Edited to add -
I'm going to add a bit about the Mini Molly that's being sold as Courtney's Pleasant Company Doll, too, just for comparison purposes.
Courtney's Pleasant Company Doll stands just a bit taller than the other two. Her face seems to be a bit more oblong-shaped, and her bangs are straighter and lay flatter along her forehead. In looking at her eyes, they're a little more rounded at the corners, have less detail painted in the irises, and her eyelashes have a different pattern than both of my earlier fabric-bodied mini Molly dolls. I think there's something a little less friendly-looking about her (maybe a missing sparkle in her eye?), but that's just my opinion and she's still pretty cute. Her neck doesn't have either a PC or AG imprint, although I think there is some kind of imprint on her vinyl lower back or bum area.
Even though Courtney's PC Doll has an all-vinyl body, the outfits for all three of these dolls are similar. Like the others, this doll's sweater has the blue and red argyle design with green accent threads, solid blue sleeves and back, and attached white collar with the embroidered zigzag design. It looks virtually the same from the front (the zigzags on the collar might just be a touch closer together?), but the back has a long strip of the no-snag Velcro which extends almost to the bottom of the sweater. The very bottom is still sewn together, so the sweater will still need to be pulled over Molly's head, but this bigger opening should make it much easier to do so. There are two labels sewn into the inside side seam of the sweater; one is the American Girl branding tag and the other has the code 1600NF.
Courtney’s PC Doll is on the right in the following photos.
The skirt on Courtney's Pleasant Company Doll also looks very similar to the others, but it also has differences worth mentioning. First, it seems to be made from a thinner material, so the hems and seams have less bulk. Second, whereas the two other skirts that I have each have a separate waistband and two seams (one seam with a Velcro closure and one on the opposite side of the skirt), Courtney's PC Doll skirt has an elastic waistline and only one seam. This doll also has two labels sewn in the skirt's side seam; matching the sweater, one is the American Girl brand tag and the other has the code 1600NF. I don't see any care instructions on the clothing labels for Courtney's PC Doll.
Finally, I haven't completely undressed this doll so can't speak much to the bloomers (at quick glance they appear to be the same or similar to other versions) or to the socks and shoes, but I did take a couple photos so you can see the comparison. You can see that the ankle socks still have the seam going up the back, adding a bit of bulkiness there. It looks like there have been subtle changes to the soles of the Courtney's PC Doll's shoes (they extend a bit less beyond the rest of the shoe), and there has also been a slight change to the upper, so that a little less of the sock is exposed between the toe covering and the strap of her Mary Janes.
Courtney's PC Doll came with plastic glasses that I never took out of their package, and also a parchment colored mini paper back book. Unlike the other dolls' books that I have, the back of this book seemed to have some special markings that showed it's a mini-book and not just a scaled down facsimile of the bigger books. The inside seems to similarly contain just a couple of chapters, but this mini-book doesn't have a title page at all - It just goes right into Chapter 1: Turnips!