The OPs dd is 11, in an 8th grade class. Mom is a single parentin a small town, with 500 kids in K-12. That's 38 kids per grade. When you have that small of a peer group, you just don't have a ton of options, and what's available will just have the same peer group over and over again.
Clearly, the school is not prepared for academically advanced kids. And the more posters argue that OPs kid may not be THAT academically advanced, the more that means that the child's peer group is even further removed from her academically. I mean, if OPs dd was gifted or bright, rather than profoundly gifted, what does that say about the school system that says they cannot handle it? It says that in a spread over 13 years, they do not have a single student that is even close to OP's dd academically. Sorry, that doesn't mean that the dd is a failure socially. It could mean that she would welcome being in a peer group that is closer to her level of intelligence. Wouldn't you?OP, I do agree with others that you need to get a quantitative feel for her level of intelligence. She could be profoundly gifted, gifted, or just plain bright. Here, 8th graders take the classes you listed (my own dd, who is in no way, shape or form gifted, took Honors Algebra in 7th) so that doesn't prove anything. Neither does potty-training or when they learn to read. But I do think that you absolutely need to find a place where you can get a larger peer group for your dd. One that will have more kids that are closer to her academic level. You say that a jobs a job, but many areas that have better schools also have a significantly higher cost of living. I'd give up the idea of raising another Doogie Howser graduating med school at 16, and instead focus on finding a high school that will work for her.