If it were me putting it in place, I would charge a standard covid levy to everyone in the country (say 5k), and then give a discount on this levy (maybe 100%) for those who are vaccinated. This way, nobody is being charged for not being vaccinated, but is being given a rebate for being vaccinated and doing the right thing.
Given I don't see any issue with this at all, short cutting to charging people who are not vaccinated is perfectly fine as well - just more efficient in admin.
Less sure about fining people, as that may add a criminal element - unsure if it does in Austria.