We mostly carry a drivers license or some other form of ID.
We have medicare cards. Pensioners and age Veterans have concession cards or health cards.
Also passports.
Its no great impost to produce a vax certificate where necessary during a pandemic.
The unvaccinated will probably be exempt from certain occupations and may have to wear masks in certain situations..
I am certain that once NSW fully opens up the govts will assess how things are going and make adjustments as necessary. If the infection numbers don't rocket restrictions on the unvaccinated will probably be eased, however if it goes the other way the unvaccinated will have to face severe restrictions so as to prevent hospital systems from collapsing. NSW will be the first to fully open up and they will be the trial that will determine what happens elsewhere. WA will imo remain as is, nice and free internally with just border restrictions until they can be certain based on NSW that open borders do not result in a wave of infections and hospitalisations.