During a global catastrophe Australia would run out of fuel within a few months, fertilizer not long after that, and soon afterwards lose the ability to grow food let alone distribute it, or keep basic services running. The lights would go out because it has no capability or even wishful thinking to manufacture advanced electronics, precision parts, much in the way of plastics and chemicals to keep airplanes, trucks, cars, computers, communication, phones, power plants, transformers, railways, or tractors running. Basic antibiotics, anaesthetics, insulin, any kind of medical or surgical tools or technologies? Don't even bother. Most people who survived the initial waves of panic and looting and destruction would soon starve and freeze to death in the dark surrounded by coal mines and fields of wheat rotting where it lies.
Also, Australia is a strategic point in the southern Pacific and Indian oceans with submarine bases and communications, air bases, signals and radar stations. It was believed to be one of the countries targeted first by the Soviets after USA if it came to a nuclear exchange. The calculus might be a bit different with China today but Australia is not some neutral party that would escape unnoticed in the event of a world war.
I don't know what would be the safest place, but I know Australia is not it. Somewhere where people can actually build and make things, and whose people might be inclined to cooperate and be capable of enduring some hardship, would fare a much better chance.
Australia is gods apocalypse testing ground....
If I wanted to hide out from an apocalypse, I'd move to Heard Island, as long as you're not bothered by the 10% tariffs.
The farm sector is at least 50% climate denialists, pretending drought and flood are events are unchanging and anyway, nothing can be done. At the same time they actively block HV transmission, wind, solar and battery projects. They are against fracking on their land/aquifer but pro fracking and coal.
For a long time Government has shielded farmers from consequences, but we have a lot of marginal land that has been over-grazed, over-irrigated and over-fertilised, and we need to change vast areas back to wilderness and long term repair.
The biggest consequences will be for export destinations. Without the huge quantities of wheat and protein we export it will be very hard for poor and densely populated countries. We are already seeing the impacts of the fertiliser shortage. Oscillations in supply from war, politics, hoarding and climate panic will see costs rise sharply. We could make fertiliser from renewables, but it is hard to compete with Qatari gas when the SoH is open.
The QLD outback is, um, interesting. Imagine the stereotypical US gun-toting religious-nut redneck and give them an Australian accent and short stumpy legs. And just like in the US they isolate their (plentiful) children and bring them up in weird bubbles with little to no contact with the outside world, and little to no job prospects apart from falling back into the same cycle their parents are in. It's really odd interacting with them, it can take weeks of effort before they'll even make eye contact with someone from outside their bubble.
Updated on re-reading: Not trying to say everyone there is like that, just that you run into a lot of them there.