My younger so was tested on certain tests at school at six and different (better) tests privately at seven.

My older son had some private testing (WISC and achievement) at 8 and repeated again at 13 with some additional scales for his ASD dx.

He also had some other testing for the birth to three program because he was developmentally delayed and some school testing at age six (to get off the DD label) Oh and something through the school to get into gifted program at 11 (a RAIS).