I don't where you are but usually what you do is find a qualified person to test them and pay the bill. I am in NZ and that is what i did.
If you are in the US go to Hoagies gifted website for lists of recommended psychologists. Since you are concerned about ASD etc someone experienced in 2e would be best. Also check with your insurer as from other people's post while testing for gifted may not be covered testing for ASD/ADHD and gifted together may be is you get a referral. In that case you may be able to affored a full work up with a neuro.