This question contains a hypothetical with a flawed premise.

Japan did not have the shipping to support a large attack on the populated areas of Australia. Brisbane is 1300-1400 miles from Port Moresby or Lae and 4000+ miles from the southernmost part of the Japanese home islands. Japan was in 1942 heavily committed in China and Burma in terms of their shipping tonnage. Getting 3-4 division strength units as far as Lae and Rabaul was just about all they could realistically manage, and these units had considerable difficulty maintaining supplies. Australia under invasion threat created something like 14 divisions, with 3 being armored (Japan did not have combat effective armored divisions). These divisions would have been fighting much closer to their logistics.

So Australia wasn't under realistic threat. Any Japanese force that could have been supplied would have been crushed by the Australian's numbers.

However, the Allies in 1942 were undoubtedly worried about the threat to Australia. After Singapore, it seemed like the Japanese arm was much longer than it really was. The allies were also hampered by their "Germany First" strategy, and they were reluctant to risk the war in Europe to make Australia completely secure.

The assets that the US was willing to commit to Australia's defense were primarily naval. Submarines and air attacks on the 4000 miles of supply lines could (and historically did) cripple the Japanese efforts to field ground forces in the South Pacific. The US Navy also committed nearly all it's carrier groups and surface forces in the South Pacific. Battles at first the Coral Sea and later Guadalcanal were fundamentally about securing Australia. The naval (and air) war was the key method by which Australia was secured. By committing nearly all the U.S. Navy, the allies avoided having to ship huge numbers of ground troops to Australia, a plan which would have been very questionable indeed if the USN had lost control of the shipping lanes east of Australia.

Because of shipping considerations, this hypothetical is a bit hard to break down. Its hard to imagine a situation where the Japanese could have invaded, and if they did, it's hard to imagine a situation where shipping would have allowed the allies to help. Probably the most effective thing the US could have done would be to fight an air-naval war over the shipping lanes, which the allies did in any case in the south Pacific. Perhaps prioritizing the Australian theater for air assets over the strategic bombing campaign in Europe would have been a strategic possibility, but the allies guessed correctly that this wasn't necessary.