Get her a single shot 22lr. She will learn to make that first shot count, the importance of which can not be over emphasized. I would get an inexpensive one and teach the values taking care of it. Youngsters tend to get distracted at times and it may get dropped, banged up, not cleaned, etc and with an inexpensive gun thats not a real big deal. I had to resist the temptation to get my kids a nice gun for starters and was glad I didn't go whole hog. For my part, as I look back, it was more of my own pride wanting to get them a nice gun to start with. IMO, kids are given too much to soon and when they get to be young adults, they go into debt to have better things right away. Start small, make'em work and wait for bigger and better. Just a little advice from a guy with a lot of gray hair.
As an added note, I just got two of my grandkids their first shotguns, both inexpensive single shots.