One of the first things that you need to do following any international move is to set up a bank account. This was actually surprisingly easy and pleasurable to do - and a lot less troublesome than in Ireland or the UK.
My wife and I have both had previous experiences (as a Brit moving to Ireland and vice versa) of getting stuck in the home address/bank account feedback loop of madness, i.e. you need an address to open a bank account and you need a bank account to get somewhere to live. Happily, the Aussies are a bit more pragmatic/sensible in their fight against fraud and one can open an account with just a passport within a certain period of arriving in the country. This alone has made the past week a lot less stressful.
On the advice of a friend, we opted for an account with NAB (National Australian Bank), which is fee-free and comes with decent internet banking, if my experience so far is anything to go by. The pain-free setup was made even more relaxing by the friendly bank staff and the fact that they were playing a pretty awesome set of 20th Century power ballads in the branch. They were even able to order us debit cards straight away - something else that Nationwide in the UK would not do for six months! I think getting a credit card will be equally painless - we just need to wait for a couple of payslips.
With a bank account sorted - and therefore a means to transfer some of our UK funds - the rest of the immigration process feels a lot less daunting.