Hi. I'm also in Australia so thought I would reply. I cannot get too in depth because I have signed a confidentiality agreement (termed the NDA on here), but if you look on Glassdoor you'll see similar to what I'm about to write, from other people also in Australia. I applied back in April and it took a full month to hear from them. So don't be too concerned if you don't hear straight away. After that, the interview process and background check took another three weeks, and it was a week after that when I received and accepted my offer. I start in July.
The Australian recruitment process seems to be (at least in my experience) different to most of what you will read on here, which is predominantly the U.S. I had one phone interview which was scheduled by email. Then the next interview was through FaceTime, again scheduled through email. Prior to the FaceTime interview they initiated the background check and had me sign the confidentiality agreement - so I had only had the phone interview at that point. Background check took about a week and that was mainly because of the Australian Federal Police check timeframe. After the background check and both interviews, there was an online conference session. The offer came a week after that. So altogether, two months from application to offer. My offer documents, again, were emailed. I did speak to my recruiter once on an actual telephone, and although she rang from an Australian mobile number she sounded American so just allow for time differences as well with processing everything, as I have a sneaking suspicion that some of the recruitment is conducted in the U.S., even though it's for here in Australia (which may explain the fact that mostly everything was emailed. Keep an eye on your email rather than for your phone to ring).
Also regarding the background check, I have been told that some questions were asked that our privacy laws in Australia prevented people from answering (again, it's conducted by a U.S. Company). Having said that mine cleared no problem. Also, check your internet speeds. They require 5mbps download and .80mbps upload at a minimum which with Australian internet is not always possible (sigh). They will have you run a test and email the results prior to any offer being made.
I found the whole process quite fun actually apart from the waiting! Patience is key.
And good luck!