the cities are reasonably compact (Melbourne has trams) so you'd only need a car if you wanted to travel further. From Melbourne you can drive easily enough to Canberra and Sydney; from Perth down to Albany and the wine country.
I think I just went through Hertz but there will be plenty of others.
Melbourne I just stayed in a motel, Perth in the inner city, can't remember their names. They were cheap at the time but the Aussie dollar is quite strong these days.