Being Australian, I can only relay what I've heard from foreigners that I've met in Australia. With that proviso, I believe that the working holiday visa that Louie was talking about is valid for a maximum of one year, non-renewable. Staying after the term of the visa would require either (i) getting officially sponsored by an Australian company or (ii) marrying an Australian. Even in those two cases, you're likely to be forced to return to your home country to apply for the new visa.
As an Australian with an American partner:
Australia has slightly different rules about relationships than the U.S. does. Getting married is one way to do it, but if you and your partner live together in an exclusive relationship for the span of a year or two you can be recognised with "de facto" status. It's a legal step between "single" and "married", and it's another legal basis on which you can apply for a longer-term visa in Australia and CAN be done from within Australia.
It is, however, just as expensive to travel back to the U.S. and apply for the de facto visa from there (Flights + ~$2k), as it is to apply for the de facto visa from within Australia (~$3k). And of course you need to be able to show that you've been in that relationship for a year or more, and that the relationship is both long-term and stable, which is out of the question for most Work/Holiday visa holders.
The de facto visa also gives you the right to live, work and study in Australia for two years, after which if the de facto relationship is still stable, exclusive, etc. you're then eligible for permanent residency.
0matt
There are self-sponsored skilled migrant visas available (which cost more, require more official qualifications, and take longer to process). At least some don't require you to leave the country. (In passing: these visas are several kinds of wrong. My government spends time and money trying to keep clever people out of my country, and requires me to spend time and money to get employees in.)
Being Australian, I can only relay what I've heard from foreigners that I've met in Australia. With that proviso, I believe that the working holiday visa that Louie was talking about is valid for a maximum of one year, non-renewable. Staying after the term of the visa would require either (i) getting officially sponsored by an Australian company or (ii) marrying an Australian. Even in those two cases, you're likely to be forced to return to your home country to apply for the new visa.