3 way coats are great - the fleece part zips out and she can wear it alone if she wants. Doesn't have to be brand name, but should have a water repellant shell and a nice warm inside.
I would also think about some base layers. That will do just as much for keeping her warm. Wool or poly blend, NO cotton, for those. I have some from the Terramar brand and Wickers brand, both from Sierra Trading post, they're not expensive at all. Not super high quality but they do the job well and come in fun colors your daughter might like.
[ETA just saw you live in Michigan, so you probably already knew that!]
Other sites that have not been mentioned -
LL Bean has very good quality items and a great return/guarantee policy, free shipping always. Sometimes not the cheapest but you can get a sale or try the outlet if there's one in your area.
Try
steepandcheap.com, they change their items daily but they've had lots of winter coats lately.
Sierra Trading Post has great prices - sign up for the deal flyer and they send you a coupon.
Backcountry.com has great reviews if you're undecided between two items - so does trailspace.com, rei.com, etc. Lots of people who report back on how they used the item and how it held up. I find those very helpful.