You have the right to ask.
You can make a case for moving her, but it is really up to the principal. You might be able to go over thier head to the superintendent, or the Board, but you would be best to get this accomplished at the campus level, and chances are that unless you can prove some kind of damage to your child that makes the Board fear that you could win a law suit, then they will agree with the principals decision because BOE's and superintendents are big picture, and steer clear of the small one when ever possible. The best course of action is to evaluate why you want to move her, make your case well at the campus level, and strategize on how to keep from alienating the principal and the teacher so that your chances are better for success. My suggestion would be to reframe how you present your case, and avoid the stance taht puts the teacher, and therefore the principal, on the defensive. Turn it around. It is not the teacher that is not working out, it is your daughter's learning style that is incompatable (or what ever the issue is.) While this may feel more awkward, it will get you in the door for a discussion, and in my experience, if principals and teachers have already sized up your agrument, have had it before, and tune you out, you are dead in the water anyway. If your presentation is different, and your focus is on your daughter, and not how bad the teacher is, then you may at least get in the door and have a chance.
I am guessing that this is 4th grade? I do not know what the issues are, but be ready for a pre-recorded message that says something like: "forth grade is a big jump in expetaction, and Mrs. Blank has a lot of experience getting children over this discomfort, even when they seem unhappy...I, we, have confidence that within a few weeks, if your daughter really applies herself, she will be much happier in this classroom, and either way, it is up to your daughter to do the work, and she will just have to get over being upset that it is hard..." The explanation may be a little different, but by and large, this will be it, and it will end with "if I moved every child who was not happy, that is all I would do all day long..."
You want your argument to be different, you want them to not be able to use the same old, same old rejection with you, and you want them to want to help you solve your issue.
Tread lightly, and schmooze, and know that every year will not be fabulous. There is something to be learned even if the teacher is not a gem, even if it is just how to survive being in a classroom situation that is not great.
M.