I think that the best place to start is to observe some kindergarden classrooms, and some first grade classrooms, and some 2nd grade classrooms. Get an idea what a range of kids in your local area are ready to do and learn at the various grade levels.
Then ask yourself if you think there would be 'enough' learning going on for your DD. If not, then you might want to get an 'Psychoeducational Evaluation' - that is a Psychologist who specializes in IQ and achievement tests to test her and see what is the best fit for her in school.
It sounds like she is also Intense - which many, but by no means all, gifted kids are. A great parenting book for that is 'Transforming the Difficult Child Workbook' by Lisa Bravo and Howard Glasser. These kids can be hard to handle!
Sounds like she is doing really well - my advice is to enjoy the progress she has made.
Smiles,
Grinity
