This is a very common problem so I am glad you asked the question.
Eruption time of primary or baby teeth varies from child to child. A baby's first tooth usually appears sometime between four months and the infant's first birthday. Some children are born with teeth and others do not develop them until they are well over one year old.
Complete agenesis or absence of teeth is extremely rare. Most likely, your child is just a late developer. X-rays would confirm that your son indeed has teeth but the problem becomes taking the pictures on such a young child. It is unlikely that a pediatric dentist could get your son to sit still long enough to obtain a readable x-ray.
I share your concern about exposing children to unnecessary radiation. Fortunately, the amount of radiation from dental x-rays is minimal. As a matter of fact, we are all exposed to more radiation on a daily basis from the atmosphere than we receive during a dental x-ray.
I tend to agree with your pediatrician and feel that this problem is not alarming. You should give it a few more months and allow time for his teeth to erupt. If your son is two years old and no teeth have appeared, x-rays may be easier to obtain and will be more accurate.