Science Fiction for a young girl. (Score 1)

Alexi Panshin's Rite of Passage is my first reccomendation. It is a novel that can be enjoyed by both parent and child. A Nebula winner from 1968 you should pick this up if you can find it. Flowers for Algernon by Daniel Keyes is also a good introduction for young people to the world of science fiction. Good Luck! and enjoy.