Good info above, but here's an alternative hypothesis, because there are a few statements here that are red flags for me:
"she is making slow progress with her reading and her writing."
Ummm... we're talking about K, right? And a kid who scored in the upper 90-percentiles on all assessments, cognitive and achievement? I mean, how much reading and writing is there, really, in K?
"She has shown signs of being disengaged and her teacher feels she is finding it all overwhelming."
"[the school] does have a very high academic standard"
I've seen it all too often that when a school says it has "a very high academic standard," that's a coded message for "We are severely drill-and-kill. We will overload your children with practice both in class and at home, and they will learn to hate learning." Place a younger-age (less EF, less tolerance for boredom), truly gifted (eager to LEARN) child in such an environment, and you can easily check off all the boxes:
[x] Disengaged
[x] Overwhelmed
[x] Struggling (apparently)
Testing this hypothesis also requires you to go to the school, meet with the teacher, see the work that is being done, and dig into how your DD's day is being spent.
Another alternative hypothesis...
Your child's social well-adjustment may be a product of dumbing herself down and working below her true knowledge level. My DD attempted something exactly like this in her K year. She was fooling her teacher, but she didn't fool us. It was very difficult for DD to convince us she didn't know how to write an "M" when her play room was decorated with scraps of paper containing full, beautifully-formed phrases she'd written at least a full year prior.
Extroverted, gifted girls will often be caught in a conflict between their very powerful social and cognitive needs. For my DD10, satisfying both has been a constant struggle for the entire family.
