Hi
The time from putting your application in to getting conformation and moving in can be as little as a week, but remember that you may not find a suitable property straight away, having a dog can be a little restrictive as we found out and you may have to sacrifice other requirements to facilitate this, though we did find that some rentals that say no pets might with a little sweet talking and paying a pet bond be convinced otherwise.
I would probably allow around a month to look view properties and if you prepare yourself an application pack containing the required information it will make the process a lot smoother, I remember before we moved down we tried to contact agents regarding properties we had seen and got no replies, now we are here you can see it is because they will not rent unless you have seen the property in person, I will ask our agent on our next inspection if overseas people can be on a mailing list, I think its due next week so will be able to answer then.
On the job front, I can only speak from my trade, I'm a mechanic, it has stared to pick up a little as we are moving into summer, there are quite a few electrical contractors around so all I can say is get a resume into a typical Australian format, make sure all the qualifications are relevant and swapped to the Australian equivalent and start emailing them out with a informative covering letter just after Christmas.
Mick