I wouldn't be nervous cos Australia is the best place in the world for backpacking on your own, especially the East Coast. If you can I would recommend flying into Cairns rather than Brisbane, cos the whole East Coast is worth seeing.
In Cairns I stopped at a place called Rosie's which was a really nice hostel with a pool and jacuzzi. Also, it was a couple of streets back from the main strip so it was a bit cheaper than some of the other hostels (I paid A$17 for a dorm with a/c, or A$15 without a/c - but that was in 2002 so may be more now).
Also you got a free voucher every night for a meal at the Woolshed so everyone at the hostel went along together every night for their free meal which meant everyone soon got to know each other.
But to be honest you'll meet loads of people whichever hostel you stay at.
