Just be cautious of some recruitment agencies as they can do bulk recruitment but often there isnt actually a position or employer. They are doing it to get cadidates on their records.
You can register with Centrelink to be a job seeker but if you walk into a Job Service Australia Provider they can register you straight away as well (I work for one) and thats where Centrelink will send you to look for work.
Were in Brissy and we like it here but Aussie overall isnt for us so we will be coming home in the next 18 months. The weather here is great especially in winter.
Not too sure about pets sorry. I imagine they would be in quarrantine for a few weeks before you could get them which would give you time to get a place to rent or what ever.
We live in a 3 bedroom 2.5 bathroom townhouse and we pay $355 rent and the average is between $340 and $390 for a similar townhouse.
Here is some info on Truck licences in QLD. It would be different in VIC or another state.
The Commonwealth Bank is probably the best and easiest to set up when you arrive. If you are with ASB in NZ you can do it before you leave NZ if my memory serves me correctly.
When we moved here we did a 'rent to own' kinda package for all the big ticket household stuff. It saved us having to buy everything and they didnt do a credit check which was great cos we obviously didnt have a credit rating in Aus.
HTH