There's a few problems with the Japan invades Australia scenario. The most important of these is the Japanese Army's hopeless supply situation. Their army, especially in Malaysia, Indonesia, & PNG, relied upon speed & a quick resolution to a battle. However, if they got into a long drawn out affair, like in the Battle of Kokoda, the Japanese lack of a decent supply line catches up with them & they are defeated. So, in order to take PNG, where the Japanese can thus invade Australia, they have to drastically improve their supply situation.
Yet even if the Japanese do completely reform their thinking & actions in regards to supply lines, they still have to find the supplies for an invasion of Australia. I don't know why people think that such an action will be easy considing Australia is the size of Europe. Even Nazi Germany, at its height, couldn't manage to control all of Europe, yet people think that Japan can conquer all of Australia will little effort. Not only are the distances invovled great, but the northern half of the country requires great effort to traverse. Any invader has to deal with everything, from thick jungle (equal to anything in PNG) to deserts stretching for thousands of kilometres.
Then there's this business over Australia losing its army in Singapore. That's completely wrong. In WWII Australia had two different armies. There was the volunteer force known as the AIF & then there was the conscript force known as the CMF. At Singapore, only two briagdes plus divisional troops of the 8th Division (AIF) were lost to the Japanese. The third brigade of the 8th Division was in Darwin & survived intacted. The veteran 6th, 7th, & 9th Divisions were in North Africa successfully fighting Rommel. Back in Australia, meanwhile, there were five divisions of the CMF along with various other support units. Just as importantly, after the fall of Singapore, the Australian Curtin goverment ordered home the three veteran Australian division from North Africa to engage the Japanese. This they did so successfully in PNG & ensured Australia was never to be invaded.
Now certainly the Battle of the Coral Sea helped tremendously in defeating the Japanese plans for PNG & any possible invasion of Australia. But then again the Japanese Navy often had their act together unlike the army. But just as Germany's situation with Sealion, even if the Japanese did take PNG, invading Australia is another thing altogether. Not only would the entire Australian army of 9 or so divisions be up against them, in other words the Japanese would be greatly outnumbered by this stage of the game, but the Japanese just wouldn't have the supplies to carry out a successful invasion of a country the size of Europe.
Furthermore, by mid 1942, the RAAF is getting substantial increases in very good equipment in the form of Spitfires, Beauforts & above all Beaufighters. As the Beaufighters clearly demonstrated in the Battle of the Bismarck Sea, any Japanese invasion fleet caught at sea would be decimated long before it hit the beaches. And the Japanese had nothing which could stop the Beaufighter whilst Australia had plenty of them to throw at the Japanese.
Of course, if the Japanese were determined to take a large chunck of Australia (say most of Queensland which would be equal to the combined land mass of France & Germany), they could provided they employed the resources. This would mean, however, an army in the vicinity of 250 000 troops, with much armour, several squadrons of Zeros, various bombers & the like, not to mention three or for aircraft carriers along with their supports & escorts. Importantly for the Allies, however, there wouldn't be much left elsewhere to defend the Pacific against the Americans counterattacking. As such, I'd expect the Americans to go on the offensive & do much damage to the Japanese throughout the Pacific. Similarly, the Japanese advances in Burma may fail, leaving the British & Indians in much better shape to defeat the Japanese in that part of the world.
Meanwhile, even with such an impressive invasion army on the move in Australia, the Japanese will eventually find themselves stuck north of Brisbane. Although it was unofficial, the obvious Australian plan in dealing with a successful Japanese invasion in northern Queensland (where the expected invasion was to come), was to withraw to the "Brisbane Line". This would force the Japanese to move over 1 000km to where the Australian army (of close to 500 000 troops) was waiting for them. So the Japanese would still be outnumbered & facing a defence line akin to the trenches of the Western Front in WWI.
Significantly, for the Japanese, their tactic of outflanking a defensive position through the jungle could no longer be utilised. Instead they'd have to attack prepared defences. As a result, the Japnese will be slaughtered. And their invasion of Australia stops around about there. Then, it just a matter of time, before the Australian forces slowly counterattack, & eventually destroy the Japanese army in Queensland, which will probably take about one year. So by 1944, Australia is free of all Japanese forces & Australian, in turn, would invade PNG driving the Japanese before them. Needless to say, however, with the Japanese wasting many resources in a futile invasion of Australia, the war in the Pacific Theatre could be well & truely over by the end of 1944.