Google the CDC Catch-Up Schedule for dose scheduling. (I'm so sorry. I can't C&P right now). It's very important to wait out each minimum interval, or your doctor will insist on repeating the dose. On the other, most (maybe all!) states want those vaxes done right away, as soon as the minimum lapse time passes. Your school district or health department can let you know for sure.
I believe that by age 6, your LO should only need 4 doses.
Can you pick and choose your vaxes in Illinois? A lot of the religious-exemption states allow only for all or nothing, so you may wish to double check on that. I've heard of parents getting around this by crossing state lines to get vaxes. But all 50 states have vaccine-tracking registries, and not all allow opting out. Imagine that. A state putting up an impediment to getting your child vaccinates...:eyeroll)
Anyway, good luck!
“It is simply no longer possible to believe much of the clinical research that is published, or to rely on the judgment of trusted physicians or authoritative medical guidelines.” - Marcia Angell, M.D., former NEJM Editor
Private Parts are Private Property!