Helena
Get in contact with a recruitment agency in the city you're going to sending them your CV. You should be able to line up an interview with the agency for the first week you arrive.
It should also give them time to line up some potential positions for you.
This is what I did when I went to Melbourne last time & I started at my new job within 9 days of my plan landing!
I don't know what the current rental market it like but get on
Real Estate, Property, Land and Homes for Sale, lease and rent - realestate.com.au and line up some property viewing for when you arrive. You can't really do this until about 10 days before hand though.