What I proposed initially wasn't a conquest of Australia but, rather a serious diversion of attention by Australia (and the US in turn) away from the Pacific theater and more important Japanese conquests. That is why I only proposed the Japanese land and take the area near Darwin along with the off shore islands. There is a single track going to Darwin and I would suspect no paved roads whatsoever in 1942. Darwin offers a port and several decent airfields in the immediate area. For the Japanese moving supplies to Darwin is not a particularly daunting task. They can haul them to Timor and then load them in small coasters or barges and either move across the Timor Sea or along the New Guinea coast then across to Darwin. Either would make unprofitable targets for aircraft and submarines.
At the same time the Australians and US would be facing the daunting task of supplying their troops at the end of that 1000 mile rail line. Of course, I'd expect it to be improved substancially. The US likely would also build some roads, even a few paved ones I'd bet. But, all this and the troops that this would support takes away from other operations. It possibly would have stalled the US occupation of Guadalcanal in favor of more troops to Australia. New Guinea likely would fall in its entirety to the Japanese.

And, then there is the Middle East. How would it have been effected when 8th Army loses some of its best infantry formations to home defense in Australia?

The scenario I proposed didn't have the Japanese taking, or even trying to take, all or most of Australia. I completely agree it is far beyond their means. But, in June of 1942 the landing of say, 20,000 Japanese troops total in the Darwin region and their move tens, or possibly as much as a hundred miles inland would have definitely panicked Australia, even if that panic was short lived to just a few weeks or a month or two. It would have forced a US response. It doesn't expose the IJN to any real risk and there was some support within the IJA for such an operation.