I think that studies have shown that when parents suspect giftedness in their children it is usually there (so if you have a hunch, it is likely correct).

That said in our own DS4's case we thought maybe high average or moderately gifted, but he tested much higher (we take this with a grain of salt as it is still early days and IQ is not stable at this age).

Since IQ has a genetic component the parents' perspective on what is "normal" or "average" may be skewed.

In any event we found testing very helpful - it is good to have an independent measurement. At 6 your son can do the WISC I think.