An oncologist treats people with cancer.
a gynecologist
Veterinarians treat animals including cats and dogs.
Obstetrician
Cardiologist
The person who treats foot complaints is a Podiatrist
A psychiatrist
ENT specialisd
There isn't a type of doctor who specifically treats doctors.
This person is called a specialist in ORAL MEDICINE. In UK some of these are located in the British Society for Oral Medicine website.
call a doctor
If you mean newborns, which I'm guessing you did, the physician responsible for that would be a neonatologist.