Absolutely not. Seriously, take a look at a map of Australia. Japan might have been able to stage a landing at Darwin or somewhere else on the northern coast, but so what? Once there they have to make there way across a continental size mass of terrain before they can get anywhere close to the economic or political centers of mass. And that terrain is, in general, fairly challenging. Forget enemy action - just getting a division of troops across that area in fighting shape is a non-trivial exercise in logistics.
The other major question is "where are the resources for this enterprise going to come from"? Most of the Japanese army was engaged in holding down China. I'll let Carl or someone else talk about exactly how many divisions and how much ancillary equipment would be needed for this job, all I know is that it would be a lot. The forces that Japan committed to South and Southeast Asia were stretched to their limit as it was, I don't see how they can afford to take a swing at another continent as well. Maybe if they don't go after India they'd have enough spare, but going after Australia means their lines of supply and communication would also put pressure on their merchant shipping capacity to get across Torres Strait.
Finally, there's a greater strategic issue: what's the point? What would Imperial Japan gain by trying to take and hold Australia? I'm not saying there are no reasons for them to do so, I just can't work out why they'd do it instead of putting pressure on India, which is the jewel in the crown of the British empire.
Frankly, I don't think they have a chance of taking Australia, never mind holding it, and thats just from a logistics standpoint. But I'd be interested to hear what others have to say.
