D.,
Nearly all 50 states (inlcuding AZ) have a right to waiver vaccines form/law due to medical , religious or philospohical (personal choice) reasons. So, your child (by law) is still entitled to attend public school regardless of whether your vaccinated them or not.
http://www.nvic.org/Vaccine-Laws/state-vaccine-requiremen...
http://www.arizonaautismsupport.org/vaccines.html
Knowing you don't have to vaccinate; some parents opt to delay vaccines until their kids are older, or space them out so that not so many are given at one time...or not do them at all. My oldest (stepson - 10) was vaccinated as a newborn/infant for the first year. He has autism. My three children who are 5, 6, and 10 have never been vaccinated and are extremely healthy. They all go to school and we just sign a waiver made available by the school - you just have to ask for it.
Don't be intimidated by the language your pedicatrician uses, or that the schools sometimes use. It's your right to have all the information and the waiver.
If you need more information, I have tons!
Best,
C.