Welcome!
What do you think about the teacher's thoughts about your daughter? Are they in line with what you are seeing? Does your daughter seem to be someone who works really hard and her school situation is a good fit? Do you see any real misfit between your daughter and her school situation? Is your daughter happy or unhappy with her current situation?
To me, with no gifted program in your district, I would think you should weigh carefully whether you are needing access to either some of the programs that you mention or to an accelerated curriculum. If so, then I think it would be reasonable to do private testing. I agree with epoh that you would probably need to find someone outside of the school system to do the testing. If your daughter seems to be thriving in her current situation, though, perhaps you don't need to test, but rather just take in what the teacher says and use it to help guide her opportunities within the school system as they arise.
