It is exactly like Russia. Sacrificing Western Australia to buy time is actually not a bad idea, as all attempts to cross the country laterally have failed abysmally. If you somehow manage not to die of heatstroke or dehydration, if you manage not to piss off any of the wildlife (including estuarine crocodiles, the largest crocodiles in the world, and the inland taipan, the most venomous snake in the world, and its relatives the mainland taipan and mulga snake, which are nearly as potent and a lot worse-tempered) if you are miraculously not killed in a sandstorm or one of the epic downpours that crop up, if you don't starve to death from dingos and hopping rats stealing your rations in the middle of the night, if the local indigenous tribes don't take a dislike to you and poison you or screw with your navigatory equipment or spear you... after that you still have to deal with the Australian military and any local populations who have formed a militia, and they will be well fed, hydrated, and very pissed off.
If you even make it ashore. The majority of the western Australian seaboard is protected by rocky reefs. A fact many early sailing ships discovered quite tragically when they ran aground. According to historical records, even if you made it ashore, between the environment, the local tribes, and the wildlife, you were lucky to make it out alive.
And don't think trying to come through the northern rainforests will be any easier. Between the monsoons, the crazy wildlife, and the heatstroke (people have literally been boiled alive in the Daintree,) well... take a look at what we did to the Japanese at Kokoda, then add in the fact that we're fighting on home ground. Yep. You're screwed.
And lets not forget that the average Aussie farmer has a couple of rifles, a shotgun, half a crate of jelly (Gelignite) and you don't want to know what else tucked into the back shed. The Aussie locals aren't much less deadly than the wildlife.
That amount of weaponry is minimal, most are better armed than that. A lot of Australian farms are capable of being independent for food and water, enormous quantities of fuel, underground tanks, and it's very common to have a well equipped workshop that can make anything from a tractor to a machinegun.
Not for nothing did Rommel say, "If I had to take hell, I would use the Australians to take it and the New Zealanders to hold it."
Of course, most enemy armies would try to invade the east coast in that case. Not to mention modern militaries have much more modern equipment like the Osprey. There is probably a commander stupid enough to invade west Australia, though. Not to mention there's a barracks over here that has a little unit called the Special Air Service Regiment. Who Dares, Wins, troper.
The east coast is where all the soldiers are. Back to square one.
Not to mention that if invaders landed in Far North Queensland and tried to sweep down the eastern coast, they'd be confined to a narrow strip of land as they moved: most of the Queensland coastline is flat, but travel inland a little way and you hit mountain ranges, rivers, and in some places enough jungle to make the Viet Cong weep. As mentioned above, jungle is what our lads in the beige berets do best.
Invading Sydney? Well the Great Dividing Range makes coming in from the west suicidal as the few roads able to support large vehicles are obvious bottlenecks. The bay area has a smallish mouth making it a shooting gallery for ships sailing through. Coming up from the south requires being able to either cross the Great Dividing Range with land forces where there are even less suitable crossing points, or being able to sneak past the city and land on the coast. Invading from the north is the same except the Great Barrier Reef isn't called that for nothing.
Invading Melbourne? Well forget any naval support, the mouth of Port Phillip Bay is one of the most dangerous stretchs of water in the world. Refusing the assistance of a pilot to get through is suicidal at best, not to mention the ADF has forts on both sides of the openning. Landing on the eastern side of the mouth runs into the problem of crossing a range that leads mostly into wilderness. Land invasion from the east and north are blocked by the Great Dividing Range again. Invading from the west requires a fair march through the Otway Mountain ranges and finding a place to land where giant cliffs don't turn the whole scene into a bizarre reversal of the Galipolli landing.