We probably should look at the school and see for ourselves and really ds if its as perfect as we imagine.
This.
It's open house season at private schools right now, so they may have one coming up this weekend or very soon. Check their website.
I advise preparing a list of questions before you go. For example, what's their policy regarding kids who are ahead of their classmates? If they have one, how do they figure out that kids are ahead, and how do they place them? If they tell you that their curriculum is advanced/a year ahead of public schools/etc., be careful. This could be their way of saying, "It's good enough." You're looking for signs of flexibility or lack thereof.
If you apply to the school and/or ask for acceleration, they may test your son. I
strongly advise finding out what kind of material the test will cover beforehand (e.g. find out which math book they use, get a used copy on Amazon or borrow one, and make sure that your son has a good idea of what's in it). Different schools use different books, and most of them look down on the books used by other schools. This is particularly true of private schools.
I'm writing this because you don't want your son to do "poorly" on their test because they have a quirky way of doing a group of things that he could learn in an hour or less.
All that said, this will be less of an issue for a six-year-old. But it's still worth checking out.
