Travelling on your own is the best way to travel, dont have to worry about what anyone else, wants. Great way to meet some new friends as well.
i would start in Sydney, more chance of a job, great night life, and loads of backpackers. + after christmas & New years the prices drop back to normal rates. $20 - 30 for a shared dorm room.
You can get free dinner at the gaff bar, win prizes, there is all you can eat pasta meals on a monday at the sugarmill, free beer at alot of the pubs when you go with your hostels.
Kings Cross is a huge backpacker mecca, and a little cheaper then the city or Bondi Beach, you also have the backpacker strip on William street, where all the car rentals, and travel agents are.
I did Oz Experience up the east coast, had the best time. Hop on Hop off bus for single travellers or couples. Its a bit of a party bus, but your here for an experience, so why not live it up. lol