Well, I would confirm with whatever schooling you are considering for after K (ie 1st grade) to make sure they will take him in 1st after having completed K at the private school, even if he is only 5.
I know you're asking about the testing, but if early k is the goal of the testing, I thought you'd want to know that some of us have had more of a problem getting our kiddos into 1st or 2nd than early k. (We had this problem last year...)
His scores will obviously be more stable once he's 6 or so...