There is no such thing as a pediatricians degree. In the US, pediatricians have a Doctor of Medicine (M.D.) degree and must pass a US Medical Licensing Examination. The typical course of study is four years of undergraduate education, followed by four years of medical school, followed by at least three years of internship and residency. You can start at any college or university that offers a pre-med track.
Pediatricians in private practice derive income from self-employment, rather than salary or hourly wages. Pediatricians who are members of a medical practice partnership may receive a base salary plus a percentage of the gross receipts. The amounts vary a lot, particularly with location, but one study (in 2009) estimated an average annual income of $163,350 for pediatricians in the US.