Looking for a house
Most property sales and tenancy agreements are done by real estate agents. When renting or buying a house, the website to look at is: www.realestate.com.au. Helpful might also be the links provided by the Australians Government regarding 'Buying, selling or renting property'.
Have a chat to people from the city you are moving to or search online for hints. Suburbs to live in vary in price and character. For example in Adelaide, coastal properties or those in the eastern suburbs tend to cost more than those in between or the North and North West of the city.
Renting a House
You should be able to find a rental property which suits your needs within 1 -3 weeks. Be careful when looking at the prices: its advertised weekly! Contrary to Swiss Law you are not allowed to put nails into walls. Also very unusual for Swiss is the fact, that every three to four month a house inspection may be done by the real estate agent. He will check on the condition of the rental property.
Be also aware that most houses in Australia are built with single-glazed windows and little or no insulation. Winter nights can be chilly!