It seems you are parenting her. I applaud your efforts. Every child needs a push. Sometimes the schools need a shove. Not everyone can see the forest...
I have a granddaughter very similar. She is 7, and has always been introverted, but totally sweet and loving, with a high functional brain, although sort of spoiled, and very hard to teach. Her attention span is only about 30 seconds, and then she refuses to participate in the lesson, whatever it is.
A previous school district we lived diagnosed her with full blown autism, and demanded she be put into a class with problem kids, kids with Downs syndrome and very low-level handicapped kids.... even though she has a much higher functional intellect.
The public school where we live now has her mainstreamed into a 1st-grade class with other kids her age. They have a reading and math specialists see her every day, and she is doing great. She can recite word for word the lines in every single Disney movie ever made.
I dread to think if I had allowed these public school dolts to put her in with the severely retarded Downs kids. Now, she is the most popular girl in her class, in the entire elementary school, literally, because she is so sweet and lovable -- even though she occasionally gets stubborn and has a tantrum over something silly.
It seems you are parenting her. I applaud your efforts. Every child needs a push. Sometimes the schools need a shove. Not everyone can see the forest...