I think the "cooped up in the house" bit wears a bit thin on anyone. When my DS was younger, I sought out early childhood classes, and since he was 3, he's been in part-time preschool. We also liked zoos, children's and science museums, etc.
But if you can't get out, maybe you can set up an activity station with all kinds of things your DD can do on her own. We have a caddy with art supplies by DS's little activity table, and he's got a little kitchen too. I don't have a girl, but I know for DS4 legos have been the best toy. Other fun toys kids can play with themselves: wedgits, gears, playdough, playfoam, moonsand. If she likes activity books, you can let her pick out some at target (workbooks or mazes, etc).
And I don't think TV is all that bad. There are some great educational shows on PBS and discovery. Also, pbskids.org has great educational games.
I wouldn't worry about if your kid is getting ahead of other kids. Just follow her lead and give her things you think she'd enjoy. If there's one thing i've learned, gifted kids don't stop learning even when you don't try to teach them anything.
Good luck, and have fun.
Last edited by st pauli girl; 11/25/08 10:19 PM.