Go to the school and find out what the requirements are for placement in the gifted program. Then begin to gather evidence that your child meets these requirements. If the school will not test your child for the gifted program, you will need to obtain sound testing of your daughter's abilities. Her pediatrician should be able to help you locate a private counselor, psychologist, or psychometrist for testing. The local university is another place to look for reliable test givers.
Keep in mind that you don't need to rely just on the school system to provide your daughter with opportunities for the gifted. Investigate local colleges to see if they sponsor enrichment programs for gifted children. Since summer vacation is almost here, you might want to look into the possibility of your child attending a summer camp for gifted children. Another idea is to let her work with a tutor who could expand her interest in a particular area.
It is great that you are working with your daughter at home. You must continue to do this. You can find more resources for educating gifted children at the following websites: Prufrock Press, and National Association for Gifted Children.
Learn more about your child's special gifts -- complete this checklist.