I found screenshots of the upcoming American Girl World app! Unfortunately, I don't know the release date in America, I think I'll call American Girl on Friday when there's no school and ask. But here are the screenshots!
These two show the doll chooser. It looks like Gabriela and Z are free to play, and Nanea is probably a in-app purchase.
This is a game involving Z's Kit doll.
Example of dialogue between two characters.
The dressing area for dolls. They cost a virtual currency called gems, which you can earn in-game or probably pay for online.