So It's "common knowledge" here in Australia we were under serious threat of invasion by the Japanese in WW2, but I don't really think the threat was that great given as I understand Japans situation at the time, fighting in China, lacking serious oil resources, fighting in west Asia and threat of the American fleet in the Pacific. Was Australia actually under a serious threat of invasion from the Japanese? To me it doesn't seem so.
By mid-February 1942 it was becoming clear to the IJN and IJA that they would shortly have control over their initial war targets. Bataan being the only place where Japan wasn’t either on or ahead of schedule. Neither the navy or army wanted to sit back and await counter attacks. The sentiment was that as long as they had the initiative they should continue to push out their defensive perimeter.
During this period there was a discussed invasion of Australia that might take place sometime after operation MO (Port Moresby). This was most strongly suggested by factions within the navy. The army however was uniformly against the idea of an invasion of Australia, as was the Prime Minister Tojo, and the commander of the combined fleet Admiral Yamamoto. So planning never got past the vague proposal stage. Instead a plan was worked out to isolate Australia by invading Fiji, Samoa, and New Caledonia in operation FS, which would follow MO (Port Moresby), RY (Nauru), and MI (Midway). Even that was cancelled after the Battle of the Coral Sea drove back the Japanese in MO, and of course Japan’s devastating loss at Midway. So FS never got past basic planing, and the forces allotted to it instead were used in the defense of New Guinea and the Solomons.
So Japan never even got around to planning an invasion of Australia. The IJA did do the equivalent of some back of the envelope calculations suggesting that they’d need additional 10 divisions and the bulk of the merchant marine to support such an invasion. But those figures shouldn’t be taken too seriously. There’s no indication that the Army was doing anything beyond pulling figures out of thin air to emphasize how insane they thought the idea was. To them it was a ridiculous idea on the face of it.
In theory Japan had enough troops and transport to do such an invasion. In practice there was no way the army was going to pull the troops needed out of Manchuria or China. Nor was anyone inclined to assign the transport necessary to support 10 odd divisions that far south. None the less Australian fears in 1942 were reasonable. Japan could have theoretically mounted such an attack, even though there was never anything approaching a plan to attack Australia.