Sure,
Down Under that means a full course of approved vaccines (one does J&J or two doses of AZ, Pfizer etc). Boosters remain optional for now... Part of that is likely due to the fact that we had such a slow roll out of vaccines last year (stroll-out). Because a large cohort accessed vaccinations late, our middle aged and younger population will only eligible for boosters this month or next. The boosters are here and people are willing, it is just a matter of waiting four months.
The vaccination data is being recorded by our Government. The public healthcare scheme (Medicare) has all of this information. In theory we should be able to retrospectively analyse the effect various vaccination outcomes (number of doses, timing, prior health conditions). In practice the data is probably difficult to access and match due to privacy concerns and the glorious navigability of various IT systems cobbled together using 1990's technology that was patched ad infinitum.
The EU have taken an interesting and smart route. Again, certificates are issued for a full course of approved vaccines (one or two dose schedules). As I understand it, the interesting addition is that the
vaccine certificates expire after 9 months after your last shot. I believe you need boosters to renew the certificate? Interestingly I dont think they have determined an expiry period for the booster shots but are reserving the right to do so.