Not that I'm disagreeing, but you're a little off
By the time invasion is possible Australia has the following Australian military formations are active and at home:
- The 6th and 7th Divisions, both AIF, home from North Africa
- Remains of the 8th Division, AIF, recuperating after heavy losses in Malaya
- 1st Armoured, active since July 1941, achieved full OOB May 1942.
- The 1st, 2nd, 3rd and 4th Divisions, Citizen Military Forces, active though with some sub-units deployed to New Guinea.
- The 3rd Motorized/Cavalry (name depends on the exact date...), Citizen Military Forces, active.
- The 2nd Armoured Division, Citizen Military Forces, forming
- The 6th, 10th and 12th Divisions, Citizen Military Forces, forming.
- Plus various other bits and pieces about the place.
So, just counting Australian troops, that's 6-9 infantry divisions depending on the exact date of the invasion; 2 armoured divisions and one motorized division. There also the possibility of bringing the 8th Division back from North Africa early.
In terms of American forces in Australia...
- The 32nd Infantry Division arrived in April-May 1942.
- The 6th Infantry Division arrived in April 1942.
So, that's 8-12 infantry divisions, 2 armoured divisions and one motorized division available.
Japanese sealift means they're hard pressed to bring more than 3 or, if really stretching things, 4 divisions to the game.
Yeah, unless the Japanese land in the Middle of Nowhere, NT/Far North Queensland the landing goes squish quickly. If they do land Middle of Nowhere, well, it's a self supporting PoW camp until supplies run out, thereafter the landing ceases to be a problem... unless the Salt Water Crocs get 'em first.
Not that I'm disagreeing, but you're a little off on the OOB.
The US 6th Infantry Division did not arrive in the Southwest Pacific Theater until January, 1944.
In 1942, US divisions that reached Australia included:
- Americal Infantry Division - 26 Feb. 1942 (as TF 6814, POPPY Force; hq and two RCTs; third RCT arrived 7 April); re-deployed to New Caledonia 6 March 1942;
- 41st Infantry Division - 6 April to 13 May 1942 (hq and three RCTs)
- 32nd Infantry Division - 14 May 1942 (he and three RCTs)
The pre-war AMF order of battle was 1-4th Infantry and 1 and 2nd Cavalry divisions, plus various separate brigades and battalions; the 5th Infantry Division was organized from separate brigades in 1941-42. The AIF forces in Australia in 1942 included the 6th and 7th Infantry (which arrived in the spring) and the 1st Armoured, which was converted (as you indicate) from a training division to a field division in 1942. The 8th Division was destroyed in Malaya; one brigade headquarters, the 23rd (IIRC) had remained in Australia, but its three AIF battalions were lost in the NEI, Timor, and New Britain, so the brigade was re-built with AMF units. There were multiple field, coast, and AA artillery units (including US Army) as well as engineers (including US Army) in Australia and New Guinea in 1942, and various separate brigades/brigade groups/fortress units/training units with home defense roles, etc.
One issue to keep in mind is that the AMF order of battle generally amounted to a cadre that required mobilization of the militia to get to anything approximating full strength; the total of AMF/AIF personnel in Australia in December, 1941 was something like 250,000 (although training varied widely; only about half of the AMF - 125,000 - had been in service for as long as six months, for example); there were another 50,000 Volunteer Defense Corps (Home Guard equivalent), including many WW I veterans.
The above does not include the RAN and RAAF, or the AIF units outside of the Southwest Pacific, notably the 9th Division, which was in Africa and did not return home until very late in 1942.
Still, it comes down to (at least) 300,000 Australian soldiers and VDC, the RAN and RAAF, and (at times) 2-3 divisions of US Army, various supporting elements, and both the USN's Southwest Pacific Force and the USAAF's units that became the 5th Air Force.
Bottom line, between the distances involved (both within Australia and from any likely Japanese forward bases, much less the Home Islands) and the Australian and American forces in the theater, plus the reality of the overstretch of the IJA, IJN, and Japanese merchant marine that were evident in 1942, there's really no rational strategy for a Japanese invasion of Australia the continent.
It's as unlikely to succeed as a Japanese invasion of Hawaii or India.
Best,