Get ready for back to the future. A few decades ago you had to present a yellow-covered international health record of vaccinations. No jab, no fly. Pretty simple. I can imagine that the government (and airlines, for that matter) to require evidence of vaccination to cross state borders. Certainly international ones.
Australia does not require local stage three testing for medicines for what should be obvious reasons. That’s what peer reviewed science is for, and federal approvals in the jurisdictions of invention. Just like aircraft type certificates haven't been (pre-max) second guessed for 25 or so years now.