What is the medical term meaning baby doctor?

A Doctor Who delivers babies is called an OB or obstetrician and gynecologist. They generally make a lot of money because they work in a speciality field. In fact, they are one of the highest paid types of doctors.
the doctor for taking out others babies from their womb is called a gynecologist

Answer: The gynecologist treats women in general (gyn=woman). An obstetrician delivers babies. Many times a doctor is both (ob/gyn). Neonatalists treat newborns as a specialty; pediatricians are often in (or near) the delivery room to treat the baby, too.