Hey @mumto2 and @Abcd  just wanted to jump in here and give my two cents. 

Unfortunately Autism has a lot of stigma around it, and just as much misinformation. It's very possible that some psychiatrists might not actually be able to make accurate diagnoses, and the presentation of autism can vary quite a lot from person to person. When it comes to diagnosis sometimes it is really helpful to get a second opinion if you're not really sure. 

Something to think about might be how a diagnosis of autism might help with self-understanding. Neurodivergent disorders like autism and ADHD can have a profound impact on a person's life, and increasing awareness of certain aspects or symptoms can help the person to make sense of themself and their identity in our neurotypical world. 

There's also plenty of online self-tests if your child is curious, and within the autistic community self-diagnosis is largely well-accepted, especially since accessing psychiatrists can be quite pricey as you have already seen! Getting an official diagnosis can be helpful for things like NDIS though as was said, so it depends what you're looking for.