[That's a good sign and supports your assessment that it's an issue of being under challenged. I ditto the advice to take your time and not get railroaded. When I said I'd take them up on their offer, I thought it was to pay for an IQ test. I'd probably pay for an independent IQ test with a psychologist who specializes in gifted children before deciding whether to go to a pediatric neurologist.
I think we will be taking my son to see a Psychologist, as the 1st step. I really like the school he is in, they just need some fine tuning. Hopefully, they will be receptive to the fine tuning.