Now this is something I don't have first-hand experience of, because luckily for me I have family who live in Melbourne so I'm staying with them for a few months.
But there are lots of hostels in the major cities that offer cheaper rates if you're staying for several weeks or months. So you can have an affordable inner-city location doing it this way. If you're in one place for the full year then it might be worth looking for a shared house, although a working holiday visa only lets you work for one employer for a maximum of six months.
If you do rural work for a second year extension then often accommodation will be included in the deal, but you'll have to see what jobs are available.