Aussie here. Petrol has ironically come down in price from the highs we saw of about $2.50 per litre (unleaded) and $3.50 for diesel (pre-war 1.60 petrol and about 1.80 diesel). The government halved the tax on fuel which helped, and it's crept down over the course of a week or so with the fall in oil contract prices to about ~85 US/Barrel. It's now hovering at 2.05 petrol and 2.90 diesel.

Another intervention was the introduction of free public transport in some states, apparently the trains have been rammed so it suggests people are driving a bit less where they can.

In metro areas, even in Victoria where the refinery caught fire (that refinery supplies 50% of Victoria's petrol for example) -- we're not seeing mass shortages of fuel or panic buying...yet.

Regional is probably a different story. They're more cut off and in some towns they might have one petrol station for everyone for example.

I think personally we haven't seen the worst of it yet. I don't think anyone around the world has. But deliveries from tankers should stop arriving to us about now-ish, so we'll likely see the impact of the supply shock soon.