Is there a simple online test to see if a child has autism?

Screeners only. If you are worried enough about your young child's behavior to be looking for an on-line test for autism, you probably would be best served by seeking out an evaluation with an expert in autism. Screeners are getting better, but assessing symptoms of autism is complicated, especially for those who have not seen many children with the disorder at different ages.
No. The autism spectrum is complicated. Online tests can give you some idea if you should take your person to an expert but if you suspect this condition at all, see an expert, don't rely on an online test. The diagnosis is too complicated.