My mom never used her machine, so I inherited hers when I was 11 (for sewing, it wasn't until 20+ years later that I took up quilting). I had taken home ec in school & then took additional sewing classes in the summer. I would say that if she has responded well to instruction -- whether classes or working 1:1 with family -- and has been using a family member's machine successfully, and really loves sewing/quilting, then anytime from 8-9 years on up could be appropriate.
My first machine was a vintage Singer. I think anything used that's been properly serviced (either before purchase or before use), is all metal parts & does a nice straight stitch would make for a good starter machine. Younger girls often get excited about the computerized machines that do all those decorative stitches, but my personal opinion is that it's easier to learn on a simpler machine. There is less to learn, less than can go wrong & fewer distractions. Plus, computerized machines are more expensive to service ... and as much as I adore my Bernina, it would feel excessive to me to spend so much money on accessories & parts for a child's first sewing machine.
The other thing to consider is figuring out a sewing station set-up. When I started sewing I set-up the machine on one of my mother's end tables so it was the right height for me. I had a stool with a back on it that I piled a couple pillows on & used that as my seat. My stitching was much more accurate when I would do that instead of trying to sew at the kitchen table with the speed pedal sitting on top of blocks. My great grandmother never made it above 4'8" and she used some kind of plant stand for her electric machine.