She sounds a lot like my son. I didn't think he fit the profile of a gifted kid (in the emotional sense) so I didn't pursue testing till he started insisting on doing harder math at school. He is definitely gifted! We live in a school district where you have to be at the 99% to get into the gifted program and I would say the majority of the kids are exceptionally mature. Personally I think the desire/intensity to learn is a better indicator (at least it was in our case).