With a private school, I'd be shocked if they handled the testing (after all, it can be expensive). I'd guess you'd need to do the testing privately.

You might check with the public school district (start with their website). Our district offers Cogat testing for admission to their gifted program (only on certain dates), and does some one-on-one IQ and achievement testing of special ed students. But here you can't call up and ask for a WISC to look for giftedness.