Never buy a child something they don't want. If she wants a guitar, get one. She will be happy with a nice used guitar.
I have been in the same place and I can help with this question - I'd recommend a shallow body Ovation - my daughter got one and loves it! The Ovation acoustic/electric models are comfortable for girls to hold, and the necks aren't too wide for them.
Example:
Ovation Applause Series AE148 Super Shallow Cutaway Acoustic-Electric Guitar and more 6 String Acoustic-Electric Guitars at GuitarCenter.com.
That is one pretty guitar!
I'll bet there are some similar on Craigslist at half the price, and in nice shape. She will be just as happy with a clean used one as a new one. Get a hard case too, to keep it in good shape.