Medicare, the basic medical insurance for every citizen and permanent resident, doesn't cover dental stuff (except emergency procedures in a hospital), so it's PAYH.
Fortunately private health insurance isn't very expensive (yet), especially for higher income earners: you have the choice of paying an extra levy for Medicare for no extra benefits or you can take out private hospital cover.
For me, the extra levy would be about $650 p.a., and full-blown private insurance (not just hospital but also extras like dental, optical etc.) costs me about $900 p.a. Given the $200 I get for contact lenses every year and factoring in just one or two other doctor visits a year, my decision for private insurance was obvious.
Still, even private insurance leaves you with a gap between the benefits and the actual cost: for hospital stuff there's a safety net capping, but not for extras. So the visit to the dentist this week left me $50 poorer, still a lot better than paying $210.
It wasn't too painful (despite me being scared of dentists and their surprises) and didn't uncover any unexpected problems. I'll have two teeth taken out in a month but both were known candidates for 15 and 7 years respectively, so no real worries.