You do not need to wait for your pediatrician to recommend a developmental pediatrician. Maybe ask your child's pediatrician for a referral if you need it. The person who recommended our child see a developmental pediatrician was NOT his pediatrician, it was the OT (occupational therapist) that came to our house in the MC Infants and Toddlers program. She had seen him for 1 month and then suggested some fisting behavior was not age appropriate for his age (11 months) and we should see a developmental pediatrician.
Regular pediatricians are not trained like developmental pediatricians, so I would just ask for a referral and get an appointment. My child is 6 and has been seeing a dev. ped. since he as 1 year old.