From: OH, USA
There was, how can I put this, exactly no chance of the Japanese invading Darwin ... and even less that they could have invaded Perth given the distances involved and their overall massive lack of merchant shipping.
Well, no chance for anything resembling what a regular person would call an 'invasion' ... that is, a large force with enough supplies to actually do something ... the Japs simply didn't have the ships to move the troops in the first place and, in the second, their MS were significantly slower than allied MS (average 6 kts compared to double that for Allied, IIRC) so it would take twice as many Japanese MS in the pipeline to have a pipeline.
There's a lot more, but even the Japanese, first rate fantasists that they were, couldn't ever quite convince themselves that invading Australia was possible.
Also note that, though it is rarely shown in any PTO game, the Australian Army, the MILITIA (not available for overseas service, for service in Australia only) was around seven times as large as the AIF, around 20 Division equivalents compared to 3 at full strength.
Sure, they were short of a lot of heavy equipment, but what there was was produced in Australia and, heck, the piddling little force the Japs could have landed would have lacked anything resembling heavy equipment anyway.
Japan invading Australia needs the help of Alien Space Bats.
Where exactly are you getting these numbers? I just pulled up the stock WITPAE map, which, to my knowledge, is correct in representation of order of battle and mostly in terms of ship statistics. I cross-referenced combinedfleet.com to make sure the tonnage and stuff was generally correct. IJN started December 7th with just about exactly 50 requisitioned civilian vessels for troop transport, with a median tonnage of between 7000 and 8000 tons. Each of the larger 1/3 of the vessels look to be able to ship an entire regiment, the lower 2/3 about half a regiment.
Without going into armchair theorizing about what would have happened if Midway/Coral didn't go as they did and the actual ability to garrison Darwin through the desert, it seems quite plausible.