You've received great advice above.

Have you looked into IQ tests...?
Hoagies Gifted Education Page is a great resource, with several links to explore on testing, including testers (by State).

I'll just add a link to a roundup on grade skips ,
a link which mentions differentiation (and other buzzwords),
and a link to a roundup on advocacy.

Once you have test results, the information at these links may prove useful in negotiating for appropriate placement and classroom experiences, to meet your child's academic and educational needs. Many parents have learned too late that partnering with a school is not a simple matter of handing them test results and trusting them to appropriately support and challenge your child. Beginning to explore these links now may manage your expectations and help you prepare, proactively.