Yeah, the angry or frantic clapping part, paired with an odd mouth/hand behavior sounds like Rhett's Syndrome, which is one of the few forms of autism spectrum conditions that can be diagnosed with a blood or genetic test (I forget which). It occurs in girls more often than boys, which is the opposite of autism in general. So your treatment plan of attack may be somewhat different. I am an early intervention teacher specializing in Autism, and mother of an Autistic teenager. As you know, teachers don't diagnose, but we see things...this is something to check out. I am pretty sure even if it is Rhett's syndrome, that you would want to start early intervention services, and ABA, etc. How is her development other wise?
Talking? Eye contact? Responds to her name by looking at you (right away), points with her index finger? Tries to get your attention to share things with you (toy, food, show a bird?) Those are the biggies. If one or more is lacking or questionable, definitely get her checked out.
You may have trouble finding a Dr. willing to diagnose her that early, keep looking til you find one who will. "Wait and see" is never a good thing to do. If she is and you wait, you have lost precious months when she could be improving, closing the developmental gap, rather than letting it widen. That being said, don't panic yet. Also look into her diet and vitamins. Are you sure she is getting enough of all essential nutrients? The reason I ask is, my older boy (not autistic) had severe facial tics, which were cured with a mega-dose of B6 and magnesium, that he had to take throughout childhood, but not as a teenager or adult. So nutrition is much more important in so-called "mental conditions" than anyone realized (the tics would be diagnosed as part of Tourette's Syndrome, which would fall into that category.) And the clap, mouth thing itself could be a large motor tic. You can get a free intake evaluation from Inland Regional Center ###-###-#### and ask for intake, to see if she qualifies for free early intervention services. If you are not in the Inland Empire, ask your pediatrician for the number of your local Regional Center. You don't have to get a referral, you can self refer. If she is diagnosed, and you are ready to panic, write to me privately, and I'll tell you what to do next. But don't discount the vitamin thing, and be aware that your doctor probably won't believe in it. B.