See below. Your child's pediatrician should be able to diagnose depression or at least agree that the child maybe depressed. They can also provide resources for diagnosis and management. Some providers are not comfortable with mental health diagnoses, and/or management, though. I would discuss with your provider.
Depends. It depends on the comfort level of the pediatrician with their level of training in pediatric psychiatry. It varies greatly for each individual doctor. I am certain if the pediatrician has any level of discomfort the child would be referred to an appropriate specialist.