Inconsistency can be a hallmark of 2e... or it can be a hallmark of childhood. I think in your case you might get good info from the testing, and then over the next few years you'll get lots of info from watching your DS's work change over time.
I'll second DeeDee's remarks about inconsistency - when our 2e ds was in K/1 we thought what we were seeing was either boredom, annoyance at work that was a lot easier than he was capable of doing, and sometimes perfectionism, when really what we were seeing was an exceptionally gifted kid who was struggling with a learning disability. It sounds like your school is very proactive and you have a good working relationship with them, so I'd take them up on any testing they offered. The reason an IQ test now *might* be useful is that you mentioned his teacher has said he's behind gifted K level in "writing and handwriting". Does this mean she thinks his writing output is less than she'd expect, or is it only handwriting that's questioned? It's tricky, because kids who aren't up to speed on handwriting skills yet or who have a handwriting challenge don't typically output as much writing as they are capable of... but it's also possible that there is more to the child's challenges than handwriting. Sometimes dysgraphic kids have both challenges, and that's where additional testing (IQ, TOWL etc) can help. *BUT* your ds is still very young, and a good place to start is an OT eval. The OT can look for signs such as odd pencil grip, inconsistency in where letters are started on paper and how they are formed, poor posture when writing, etc. Whether or not a child has dysgraphia handwriting OT can help with that - although OT alone (in my experience) will never help a dysgraphic kid *enough* to be able to express their full breadth of knowledge via handwriting.
Someone mentioned above that dysgraphia etc aren't typically diagnosed before 2nd grade, and our ds wasn't diagnosed until late in 2nd grade - *however* he had previous IQ testing for a gifted program, and the discrepancy in IQ score (dip in processing speed subtests) that is a clue to dysgraphia was absolutely present in his previous testing, but the tester paid no attention to it because he was young, not in school yet, and no one had any reason to suspect he had a challenge with anything. I've seen posts by parents who's children are diagnosed with dysgraphia as early as kindergarten on dysgraphia-related websites, so if you have a concern, definitely follow through with an eval.
Re the question of private vs public, I generally agree with all that was posted previously, but wanted to add - our ds has had IQ testing both privately and in school and his profile is almost always identical. I didn't particularly like the school psych that did his IQ testing, and I'm sure the psych wasn't used to testing gifted kids, but when I was nervous about the testing and talked to our private neuropscyh she gave me what I believe is good advice: the psychologists employed by the school district are professionals just the same as private psychs are. You may not have a choice in which psych tests your child, and you may not have picked the same person had you had a choice, but the psych, as any professional, is not going to purposely try to manipulate scores. You may not get ideal testing conditions, but you could also have an off day with a private psychologist.
There was also a mention previously of school districts purposely trying to show there *isn't* a need for services - and we've been at one of those schools! What we've experienced though wasn't that testing and evals were administered in a way to make it look like services weren't needed, but rather the offer of giving specific types of tests/evals wasn't made unless we requested it, and when the results were presented, they were reported in a way to obscure anything that would show there was a need.
Good luck as you go forward - it sounds like you have a caring teacher and good support at school!
polarbear