Ditto what Dottie says. Plus if you do it privately, you control what info the school has access to.
About the nuero psych. Big sigh....where do I start.
When you are very very very smart, like yourself! I believe you have an incredible ability to compensate for things like learning disability. So the slippery slope is, when is a learning disability really a disability.
Different people have different opinions about this. I always have a hard time because I think both sides have validity.
When a child is expressing the frustration that your child is, I would start the process.
We did so for our DD6. She has not gone to a nueropsych yet, but has had developmental vision testing which uncovered a learning disability that I don't think the school would have ever uncovered.
Plus a neuropsych can give you what you need to compel the school to give your daughter an IEP, if needed.
Upon hearing of DD6's experience, our pediatrician told us L.D.'s are highly hereditary, just like giftedness is.
I see what you are saying about the homeschooling. Again, DD6 is similar. When we homeschooled over the summer, though, her frustration decreased. I think because I could tailor my teaching style to the different way she learns. Once she realized this, the resistance melted away.
Homeschooling will allow you to test her out of material she is already proficient at, which means possibly, less work for her.
My biggest frustration with public school is that both my daughters are required to do work they are already proficient at. DD8's teacher told me: Because everyone else has to do it.
This infuriates me to the core. Remeber that old Hulk show on T.V. when we were kids, Bruce Banner started spinning around and then turned into the hulking green monster with a big roar? Yeahhh, that's how some of those school comments make me feel.
An individualized education plan either at home or school will give your daughter a more realistic education plan, whether at home or school. Hopefully.