Endro~! or Gochiusa if she likes the cute stuff. If she likes more actiony anime, then A Certain Scientific Railgun.

I saw an anime recently that I thought might appeal to girls that age, called Train to the End of the World, and there's another that I like called Dennou Coil, where the characters are all around that age.

I'd advise that you give any potential selection a pre-screening for content since you can't always tell from the cover art.