Jen, for a lot of kids that are deep thinkers, school is difficult. School can be a lot about output, and just cranking out the work at a high capacity, which isn't the learning style of my daughter, and perhaps yours. A child who really likes to examine things is interested in looking at something 360 degrees, not just cranking out more pages of homework. This only gets worse as the child progresses through the years. I don't know if you feel like this applies to your daughter or not.
Also, your daughter's reaction to going to another school is so positive. My daughter was the same way. When she visited the private school in which we subsequently enrolled her, she jumped into the car and said, "I want to go to school here." I think you are making the right decision, and you will not regret it at all. I would rather have a more well adjusted daughter than more money any day, and I know all of us on this site agree!
Beanma, sorry to disagree with you, but I wouldn't recommend leaving the ld school midyear.
And for everyone, I wanted to mention something about public schools these days. (I am a teacher.) Unless you live in a state that has opted out of the No Child Left Behind laws, i.e., your school system says "no thanks" and gives up the funding from the government, your school system is RULED by this legislation. Every school in the U.S. is supposed to be "proficient" by 2014. And many schools in fine districts are not making AYP (Annual Yearly Progress) because of a small subset of students, whether they be new to the English language, Special Ed, or whatever. In my school, our very fine principal has been told she will be reassigned if our school doesn't make AYP this year. IT IS ALL ABOUT THESE TESTS.
Also, please consider this. Schools are in a time of high need, and reduced resources, because of the economy. Class sizes are usually larger than they should be. If your child isn't going along with the flow, the teacher most often has the very best of intentions, but there are so many students with a variety of "issues," it can be hard to give everyone the attention they need, and to call the parents to boot. I called 2 parents yesterday, and 1 of them tried to make his child's problems my fault, and was very unpleasant, when I was going out of my way to reach out to him about something that was really pretty minor (his child is always sleepy in my class, and cannot focus). So teachers can be wary too. We go into teaching because we love it, but if you want an easy job, please look elsewhere!
I think there is a parallel in the medical system these days. You really have to advocate for what you need.