To become a pediatrician one would have to graduate highschool and then attend college for four years, go to four years of medical school, be an intern for one year, complete a two year residency, and then take an exam.
8 years
Harvard
You would have attend about 6 years of college before you can become a Astronomer.
Upon considering your question on becoming a 'pediatriciam', I would recommend that you take as long as you can to study. Medicine is an important field and attention to detail(s) is critical in that profession; in your quest to become a pediatrician, you should not rush.
To become a pediatrician you must complete Medical School. Princeton University does not have a Medical School. If you intend to be a pediatrician and want to attend Princeton, you would take a Bachelor's degree as a Pre-Med student and then apply to a Medical School, eventually specializing in Pediatrics.
To become a pediatrician takes many years of college education. You would first complete a standard four year Bachelor's degree program. Then you would go on to complete four more years of medical school to become a general M.D. The final step to becoming a pediatrician is to complete a three year residency, after which you would pass an examination to be certified to be a pediatric doctor.
Four to eight years of college would be required to be a forensic toxicologist.
Considering that there is about 13 years of college required to become a MD Pediatrician, if one started college at age 18, then that person would be 31 before they graduated medical school. It would be impossible to have your MD license and practicing pediatric medicine at, say, age 21. The right to become a pediatrician is not based upon a minimal age, rather based upon years of education and residency completed.
Any medical school will give you a medical degree. You can attend any of them, and once you have the degree you would apply to a residency training program in your area of interest - in your case Pediatrics (3 year residency). Any U.S. medical school will get you to that point. I would work as hard as you can in college so you can apply to get into one of them after college, and would avoid the Caribbean schools if possible.
A neonatologist is a pediatrician. You would go to medical school and follow all the residency programs to become a specialist in the field.
It doesn't matter if you attend an allopathic or osteopathic medical school. Both can become pediatricians and obstetricians. But if you want to become both, you would need to complete two residency programs.