I mean, IANAD but I would definitely get a professional diagnosis before acting on the assumption my child has a specific medical condition...?
The right next step is to get an actual diagnosis, in my opinion. You might be off-base in your suspicions, or it may turn out that your child is more affected than you suspect.
Autistic people are routinely over-medicated, and that over medication one reason for the difference in life-span for autistic people.