This sounds very similar to what DS went through in public school. Kindergarten was fine (he had an amazing teacher), but first and second grades were progressively worse. He knew all the material and then some, but would still fail the timed math tests. His work, when he was willing to do it, became sloppier. It was thankfully(?) because of his increasingly disruptive behavior that the school was willing to do a comprehensive evaluation, and his giftedness was confirmed.
After the school realized what they were up against, they were more willing to make accommodations. But it was too little, too late. They tried some subject acceleration, but they didn't give him the support he needed to catch up and not freak out at suddenly not knowing all the answers. There was talk of grade acceleration, but that didn't pan out.
Ultimately, we wound up pulling him out of school before the end of 2nd grade, and we're now on our first year of homeschooling. Life has gotten so much better.
DS is also on a GF diet, which seems to make a bit of a difference in his frustrations. We tried a dairy-free diet for about a week, but that proved to be too frustrating for DS.
One recommendation is to find a gifted group in your area, so you and your daughter can start meeting similar kids. DS had very few friends in school (most of the kids just thought he was weird and avoided him). The kids we see now on a regular basis are not only more similar to DS, but also much more tolerant of his quirks and interests.
Asking the school for a comprehensive evaluation also helped us a lot. We had gone to a local expert in gifted kids, who recommended we do that first, rather than spend thousands of dollars on his office. Definitely good advice! We knew we had a smart kid on our hands, we just didn't know how smart. The recommendation is to make the request in writing, although I don't know what the laws in your state are like (we are in California).
There are a number of books out there that might help you figure out what's going on. Some that helped us were "Raising Your Spirited Child" (which I read long before I realized DS was gifted) and "Living with Intensity."
