Depends on your definition of best....
The cheapest fares will all require a one way ticket to another RTW starting point.
In the case of One World, the closest discounted starting point would be Japan (with a ticket that does allow passing through Australia) ex Japan a DONE4 is US$5589 PLUS taxes and airline add-ons. Starting in Australia US$9175 ++++ Add 50% to convert to AU$$.
May you find a way to do inexpensive wandering
Fred
Hint: flyertalk has a one world forum dedicated to the subject
Do you have a specific carrier in mind? If not your best bet would be a round the world ticket offered by Star Alliance carriers such as Singapore Air. The fare basis code is CCPSTAR1 and it works out to $9600 AUD. These fares generally cannot be constructed via a simple Expedia or Google Flights search you'll need to look for something like OTA Matrix or a travel agent who can construct these fares accordingly. I would also recommend looking at RoundAboutTravel, a travel agency that was previously covered by AFF which provides this type of ticketing services. For instance, searching their site I see that Lufthansa business class round the world tickets start at $6971 including taxes.
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