Australia is a nation of travelers and at any one time, 5% of the Australian population is living overseas. A ‘gap year’ between high school and university or work is fast becoming traditional and Australians are understanding of lost and slightly bewildered travelers (something similar has probably happened to them at one stage)
You should be able to find at least two or three hostels in any major regional centre and the Youth Hostel Association maintains a strong presence. Many travelers begin their journey in Sydney and work their way up the east coast to Cairns or Port Douglas. There is work to be had on this route and some employment agencies cater for backpackers. Fruit and vegetable picking work is especially common.
Australians are generally a helpful lot and may point you to attractions that you wouldn’t otherwise know about. Talk to the locals. In most cases they will be happy to help. People trying to rip you off are the exception rather than the rule and any crime committed against you is more likely to be a crime of opportunity rather than anything fraudulent or malicious.
It’s unlikely that you’ll be invited to stay at an Australian’s home unless they know you already, however they may provide basic accommodation if you’re not too frightening/ugly/smelly: a shed, tent for camping or perhaps even a small berth on a boat if they have one. Beer and spirits (especially in northern parts) may create an instant rapport.
The period between December and February is Australia’s summer holidays and tourist spots will be busiest at this time. The Big Day Out is a popular music festival held in major cities and watching the fireworks in Sydney on New Year’s Eve is unforgettable, provided you find a good vantage point about eight hours beforehand.
For one of the largest nations in the world, Australia’s population is tiny but that’s what makes it such an experience. Where else can you travel across cattle stations thousands of acres wide, wander deserted islands untouched by the grubby hands of greedy capitalist investors or look up at the stars in the desert knowing that if the world as you know it ended, nothing where you are would have changed?