I agree that 9 weeks is a long time to a child, especially a very young one. I am not sure how common this is across all groups of kids, but my son did start to have problems in first with not liking the teacher, he didn't have many friends (according to his count, zero) he did ask about homeschooling as well, although not every day.
I don't think his first grade teacher was a good fit; the teacher said lots of kids in 1st don't really make friends until later years (2nd, 3rd). I thought at the time that was ok information, but my son was still sad and not fitting in.
Things were better in 2nd and part of the reason was that I told him the school was going to do an assessment to see if he could take an extra class (early years gt program in our county). He was really excited about that and hung in there in expectation of it working out; it was a little bit of a hair splitter but he got in during the last few weeks of school and was really relieved and happy. He is doing well with the program this year, 3rd, he is excited about school again. Plus his regular classroom teacher is turning out to be a gem.
Your child might be more in need of greater changes faster, however - my ds' story is just one. Things are working out ok for this semester, we are seeing how things go.
I don't think the stomachaches and the questions about homeschooling are entirely normal..
Also, someone else on the board might have good advice on which sorts of tests to look at having done - there are so many it is pretty confusing to me. So far we have just gone with what our school normally does.
Very best of luck for you and your dd!