Have you talked to a pediatrician about off-label vaccination? My understanding is that there are various barriers prohibiting this; this op-ed says there is a CDC vaccine provider agreement which forbids the practice - https://www.thehastingscenter.org/with-pediatric-hospitaliza.... But I have no idea how often it's actually happening.

The major downsides are that you'd be missing out on information about side effects from vaccination, and on possible clinical-trial data that might show a different, better, dosage in your kid's age range.