Upvote:3
There are a couple of companies offering insurance to long term travellers including work and holiday workers or round-the-world tourists.
Avi-international targets all nationalities but requires you to be under 35 - which should be the case for a work and holiday visa.
World Nomads apparently is not clear on that point for us citizens even though it covers working holidays for other countries' citizens.
There are a few others that you should be able to find through a search engine.
Upvote:6
There are options with local health insurers for $19-$25 AUD a week. This seems to be a common choice instead of getting travel insurance, however this will depend on your circumstances.
If you lookup "health insurance australia visa" you should find them.