Gifted Child

Our son is 6 yo.

At home, he’s been telling us for months now that school is boring.
And he’s been experiencing a lot of intense emotions about it (the emotions only at home).
For me, the intense emotions come from him thinking that he needs to be “perfect” and have perfect behavior at school. And that he can drop the tensions at home.
Also, him feeling boredom is because he is thinking that the pace and the material given to him at school don’t fit with his need to learn more and him being curious about a lot of things.

His teacher sees him as “a perfect student” with a “perfect” behavior and “perfect” skills.
As we brought this emotional problem, she suggested to arrange a different curriculum for him.
But, we need to provide her with the proof of his giftedness by administrating an IQ Test to prove whether or not he is gifted, as well as to determine his cognitive strengths and weaknesses.

I am feeling confused.
On the one hand, I have this thought that I can help him manage these intense emotions, we don’t need the school’s help for doing it.
On the other hand, I see that this idea of proving the giftedness, is an attempt to change the circumstances. And I am afraid that by doing this IQ test (and I know already that he is gifted) we put on him this label of giftedness all his life. Also, do we really need to prove anything to anyone?

The result I want is being able as a parent to help him feel supported and loved.

And my question is : by refusing to provide the proof of his giftedness, am I really supporting him?