We have taught our 6 yr old to tell police officers "my name is ... I have autism." But I don't know if he understands what autism is. We explained it to his sister when she was 6 since she saw the meltdowns, SIB his brother displayed and the difficulties he had in speech and socializibg. Plus it helped us explain why we spent more time on him than her.
I think it would depend on how high functioning the child is.
With our 13 year old, she was in the Dr's office when he gave the diagnosis and she was 9 going on 10, so I think she has known since then.
However in the past 2 years we have encouraged her to advocate for herself at school, things like reminding or telling teachers that she has autism so that they might understand her better, and to help them understand that moving desks or changing time tables or assemblies are things that make her very stressed and upset, because of her Autism.
While adults can often be less than co-operative with children on the spectrum (they think they are just "bad" kids for some reason) I find this strategy has helped this year, because with all of the supports now in place she is doing very well in the curriculum so that educators can forget that she is on the spectrum and get personally offended or upset when she doesn't react like a "normal" kid to things that would be no big deal to a "normal" kid.
Hope this helps.
My daughter is 8 but we don't bother explaining it her because she doesn't question it. She's not high functioning so what's the point? I actually her say the words "autism" and "meltdown" first this week while watching so YouTube video of a meltdown or tantrum so I think she doesn't need a mirror when she sees other ASD kids in school or videos.
My son is almost 5 and we still haven't said anything to him. We don't beat around the bush if he is in the room and we are talking about it, but he isn't paying attention. He really wouldn't understand it yet either. He has a hard time understanding a lot of things. You really just have to make sure they can understand it. I have to say I think he might be close. A month or so ago it was like the one really nice day out so we went to the park. It was crazy busy and he doesn't do crowds well, but he really wanted to go. We ended up leaving in tears and then when we got back to the car he broke down apologizing to me (he does that A LOT) and saying, "I don't want to play with those kids...and I don't know why!" So I think he can notice something isn't quite right, but since then he hasn't said anything. So we wait.
He won't understand. It will probably be years before he notices anything that makes him different.