Just a bit of caution, any physician or mental health professional "can" diagnose autism, but shouldn't without specializing in it. There are so many overlapping conditions/variables, OCD, child abuse/neglect, giftedness, ADHD to give a few. A similar example, as a mental health professional, I cannot tell you how many parents come to me saying that the school has said their kids have ADHD, when it is something completely different (most often intellectual capability that doesn't match what school teaches to). The school is not qualified or trained to push that, if you are concerned, I would ask your physician for a referral to a specialist.
Some things I would look for is how do they seem to engage with people that they can connect to (which may or may not be their classmates), eye contact, early childhood development, repetitive behaviors, etc. There are so many similarities between giftedness and autism, it's important to rule those similarities out.
