Qualifications
As you've probably guessed, child psychology goes way beyond "being good with kids." If you want to mold young minds, you're gonna need a doctorate, and all the school below that (high school, bachelor's, and master's degrees).
To B.A., or to B.S.?
Short answer? It doesn't matter. B.A. degrees (Bachelor of Arts) are all about human behavior and thought process—great for counseling, social work, or child development. A Bachelor of Science, or B.S., is more about "the hard facts," brain function, genetics, medicine, etc., and it's great for training for a job in research. But either one can help you become a leading expert in zombie neurology.
Put the "grad" in grad school
A master's degree is optional. Although many Ph.D.'s have master's degrees as well, it isn't necessary. If you want to take the really "science-y" route, the one with all the math and numbers, an M.S. is for you. If you're all about the people, an M.A. will be just fine (source). School psychology can require its own master's degree in...well, school psychology.
The good news is, a psychology undergrad degree usually isn't always essential to enrollment in master's programs, so if you're late to the psychology party, it's not the end of the world (source).
Practice, practice, practice
Before you can get accredited, you'll need to put in the work. Most states require around 2,000 hours of supervised practice during an internship, and another 2,000 hours in post-doctoral practice (source). But we understand that this sort of thing makes you perfect, right?
Is the doctor in?
Ph.D., or Psy.D.? If research is your thing, a Ph.D., or doctorate in philosophy, will teach you all there is to know. Or, you could go for a Psy.D., or doctorate of Psychology, which lets graduates devote all of their brain cells to learning how to practice on patients. How to decide?
Ask yourself whether your heart lies more with breaking new scientific ground (Ph.D.) or packing your clinical toolkit with Psy.D. knowledge to directly help your patients. In any event, make sure your doctoral program is APA accredited, or you'll be in hot water later on.
Testing, one, two...
Oh, good, you're done with all that school. Time to test your knowledge...literally. Enroll in the impressively named Examination for Professional Practice in Psychology (EPPP). Easy peasy, right? Then all you have to do is apply for licensing in the state of your choice and wham—you're a psychologist.