Hello there! An invasion of Australia did figure into some Japanese military plans, but it never appears to have received serious consideration. To be sure, shortly after the attack on Pearl Harbor, Admiral Yamamoto did order his staff to draw up plans for future invasions of Hawaii, Ceylon, and Australia, while Admiral Yamaguchi Tamon, commander of the Second Carrier Division, proposed an even more ambitious plan to Yamamoto in February 1942. The "Yamaguchi plan" called for invasion of Ceylon in May, which would be followed by landings on Fiji, Samoa, New Caledonia, New Zealand, and Northern Australia in June and July. Japanese forces would then seize the Aleutians, Midway, Johnston [Atoll], and Palmyra islands in November and December. The invasion of Hawaii would commence in December 1942 or January 1943. Of course, these operations would require Army support and resources, and Army leaders flatly rejected the Navy's proposals at an interservice meeting on February 27, 1942. As such, Australia was never under the threat of an imminent Japanese invasion. [1]

In December 1941, however, the Army Ministry's Research Section had outlined goals for the eventual occupation and administration of Japan's "New Order in East Asia" in a document entitled "Land Disposal Plan in the Great East Asia Co-Prosperity Sphere." Under this plan, all of Australia and Tasmania would be under the jurisdiction of the "Australian Government-General"; New Zealand, Macquarie Island, and "[t]he sea, south of the Tropic of Capricorn and east of Long. 160° E., as far as the S. Pole region" would belong to the provisionally-titled "New Zealand Government-General." For context, these grandiose visions also included an "Alaska Government-General," which incorporated Alaska, Yukon Province of Canada ("and the land between that Province and the Mackenzie River"), Alberta, British Columbia, and Washington State, as well as a "Government-General of Central America" encompassing Central America and the Caribbean (!), though "[t]he future of Trinidad, British and Dutch Guiana and British and French possessions in the Leeward Islands [are] to be decided by agreement between Japan and Germany after the war." The Army apparently believed that most of these conquests would be made twenty years later in some future conflict, after Japan had already secured the Philippines and European colonial possessions in the Pacific. [2]

Again, the Army and Navy plans seemed unrealistic from the get-go, though it's rather interesting that they were contemplated at all. On the other hand, we shouldn't belittle the fears of the Australian and American governments; the early months of 1942 were a bad time for the Allies in the Pacific as the Japanese won victory after victory and advanced southward.

I'm sure some other users here know more about the specifics of these plans and operations. I hope you find this helpful, nonetheless! :)

[1] John J. Stephan, Hawaii Under the Rising Sun: Japans Plans for Conquest After Pearl Harbor (Honolulu: University of Hawaii Press, 1984), 92-106.

[2] Richard Storry, The Double Patriots: A Study of Japanese Nationalism (Boston: Houghton Mifflin, 1957), 276. The "Land Disposal Plan in the Greater East Asia Co-Prosperity Sphere" (I.M.T.F.E. Exhibit 1334. Transcript, pp. 11969-73) is reproduced in Appendix II, 317-9.