Honestly the best way is to get a visa, and even then you're not likely to get noticed until you're in the country.
My husband is a mining engineer which is really high in demand. We applied for a permanent visa on our own, and he applied to lots of jobs while waiting for it to come in. No one would even look at him while he was out of the country. Even once he had the visa they either didn't notice or just wouldn't look at him because he was still in Canada.
Once we had the visa and arrived in Australia then he had lots of people interviewing him. We sold our house in Canada, quit jobs and then came over for a month trip, hoping to find a job while we were here. He would one the first few weeks so we stayed.
I'm sure that you're not thrilled with my advice, but I'm just telling you what it was like for us.
For jobs look at:
www.seek.com.au
For visa info:
http://www.immi.gov.au/
For visa advice and info on Australia:
http://britishexpats.com/forum/forumdisplay.php?f=54
This is by far the best website for getting help with visas, jobs, info, etc. It's not just for people from the UK so feel free to join in.