She is a really cute girl! Good job for looking for advice ;0)
I highly advise you to take her into your Vet. It sounds as though you haven't? The Vet would give you a correct estimate of her age. It's completely, completely illegal for the breeder to sell her at 3 weeks of age! In Cali, I know a breeder can get fined/jailed for selling pups under 8 weeks, because weaning is supposed to begin at 4 weeks. It also sounds like she needs to be de-wormed. Pups are supposed to be de-wormed bi-weekly until they are 12 weeks old! She also needs her shots and all of that, if it hasn't already been done. Shots, dewormings, and check-ups are SUPER important for your little girl. And be sure not to allow her to play with strange dogs or walk around in strange parks, she can pick up Parvo (which is very deadly) at her young age... until she gets her 12-week shots.
I would suggest the good quality kibble from the specialty store, for sure. Purina is basically like feeding her Cap'N'Crunch every day - full of sugars, fillers, corn, soy, by-products (which is pretty much only a small percentage of meat), etc. It is acceptable, but definitely not ideal at all. It'll be way easier for her to gain weight on good, wholesome food! Wonderful brands are California Natural, Innova, Chicken Soup for the Dog Lover's Soul, Wysong, Nutro Natural Choice, Wellness, Merrick, etc. Feed your puppy just about as much as she will eat... as long as you get her health cleared by a vet. Add water to soften the food and add the same kibble brand canned to add calories and softness.
Good luck, and please keep us updated!