Her teacher has been having her do additional work that is at a higher level as well as higher expectations than the other kids
To some extent, differentiating like that is good. On the flip side, I object to the additional part of it. If the teacher can see that she is far enough ahead to need more challenging work, then she should be just getting the more challenging work as a substitution for the regular work, not in addition to it.
The more correct answer I suspect is to look at some form of acceleration. This will be highly dependent on your state and local school. That said, with her being advanced in the academics, one of the older in her class, and unsatisfied with the pace of school as it is, she would likely be a solid candidate for a whole grade acceleration. It might not fix things, but might at least help.
I would recommend reading some of information from the
Acceleration Institute, which is part of the University of Iowa, that is it isn't some crazy independent group but a reasonably respected academic institution. The Nation Empowered reports gives a very good overview of the current state of the research on grade acceleration. They also publish the Iowa Acceleration Scale, which is a guide for evaluating a student for whole grade acceleration.