A little late to the party. We had our son tested at ~3.5y.o. because he wasn't in school at the time and we didn't have any teacher evaluations for pre-k applications. It was a good decision for us.
It's hard to say that you should test your son based on the shared information.
My first question would be to find out what the school district or state offers in terms of individualization. Look beyond the standard gifted stuff. My second question would be about the kindergarten itself and what the teacher says he/she can do to challenge him based on his current level of accomplishments.
I like the "So what?" criteria. If you test him and get a score, regardless of what it is, so what? What do you intend to do with the score that you couldn't do without it? If you have a clear answer then there's your reason to test. If you don't have a clear answer then maybe wait.
Like others have noted, my understanding is that the sweet spot for testing is a little bit older than your son is right now.
