If your child at 9 is willing to try, then she's ready. One hard lesson I had to learn is that I may not be my child's best teacher. We struggled through fiddle, guitar, and piano together; it wasn't until she began flute lessons at school that she discovered the instrument of her heart. The band teacher isn't the best in the world so we started her with a private teacher and now she's loving it! Do I play flute? Yes, I do- but I didn't try to teach my own kid!
The smaller sized guitar for the smaller-sized player is a good idea, but Giac is right that the quality should be pretty good. Good luck!