I just went through this last Christmas with my 10 year old niece. She asked for a sewing machine for Christmas "so I can be like Auntie." I agree with many of the responses that at her age she is ready for an adult machine.
I live 4 hours from them, but during one of her school vacations I arranged to visit a few days for "lessons". I cut and put together a few projects at home and brought them with me for us to make. A pillowcase, 4 inch square blocks which we sewed I to a pillow, and a place mat. She was just thrilled. She has also taken lessons at Joann's. Also it was recommended that they seek out a local quilt group who could provide instructions. Hope these are helpful tips. These young girls are the future of keeping quilting alive and thriving.