Qualifications
Undergrad, medical school, internship, and residency (source). That's about eleven years of school and training. Some medical schools offer programs where your undergraduate education is combined with your medical training, but even still, you're looking at a minimum of eight or nine years of postsecondary. After that, there's becoming licensed by passing the United States Medical Licensing Examination. and completing a residency term.
Once all that's done, you can begin pediatricizing. (Please don't look that up. It's a word. We promise. Maybe.)