Pediatric nurses would graduate from a nursing program which could be either an Associates Degree Program or Bachelor's Degree. I would recommend that you get a four year degree (BSN) as many hospitals are encouraging nurses to go back to school to get their Bachelor's Degree and some do not even hire Registered Nurses if they do not have this degree. Once you have graduated as a Registered Nurse, there are some hospitals that have internships in regards to specialties and this would include pediatrics.
It would be very helpful for you in preparing to be a pediatric nurse, to have some good experience with working with children. This could be volunteering at a Children's Hospital, donating time as a big brother in a "big brother, big sister program", or similar volunteer projects. This allows those individuals that interview you the ability to see that you have already had some solid interaction with children and this will helpful in your pursuit for a pediatric career in nursing.
Hope this was helpful and good luck in your decision making as your pursue a career.