My son is 2.5 and unvaccinated. It has never been an issue. Different states have different requirements. You are talking a military base, though, and they can have their own rules. I would think that a medical exemption would be allowed
Here is info on the state laws:
http://www.immunize.org/laws/dtap_childcare.pdf
"Although exemptions vary from state to state, all school immunization laws grant exemptions to children for medical reasons. Almost all states, except Mississippi and West Virginia, grant religious exemptions for people who have religious beliefs against immunizations. Twenty states allow philosophical exemptions for those who object to immunizations because of a personal, moral or other belief."