So surprise, surprise...DD isn't a very social child. She will join/allow same age peers to join in highly preferred play, likes to watch kids doing physical play like swinging/going down slides, etc, but is otherwise content to play solo. One exception to this is younger kids. If a younger child is interested in something she is doing she seems to love to teach them how to play with something regardless if it's something she is really into or not. Anyone notice this with their children?
Re: ASD parents...do you notice this?
Ditto above. Lol, I remember when he was 4 and going through his Clay Jam phase and he couldn't stop talking about it. He was "best buds" with 3 year old. I overheard the 3 year old say "tell me more about Clay Jam" and the look on DS's face was priceless- like he had found his soul mate. DS also tries to play with older kids and it doesn't end well.
Your description of your DD wanting to teach the littles reminds of nurturing little girl behavior, wanting to be Mom to the littles.