In my experience, you will need to take the lead on the advocacy. Teachers have huge classrooms of kids to worry about, and if a student is doing well, they will be the least likely to get attention. And most teachers will not come across kids who are many grade levels ahead in a subject, and they won't "get" it until the scores on their own tests really sink in. Or if your kiddo does something amazing (which doesn't happen as often as you'd like, when you're trying to convince teachers!)
As for what to ask for in subject acceleration, I would really try to find a teacher who is good at differentiation. The grade level won't matter quite as much. How well/fast does your DD write? That may be a blocking point, depending on how much writing is going on in a particular class. My DS was really bad at handwriting, and he's still behind.
If it turns out that there is not an appropriate class for your DD to accelerate into, there are other options. Can the GT teacher help select materials for in-class differentiation? Can the GT teacher get a group of similar kids together across grades for reading?
I would hope that the MAP scores would be sufficient to qualify for the IQ testing, as the scores show she's several grade levels ahead of her age-mates. Good luck.
