Award space on the Aus-US return routes are very difficult to come by on all carriers. You can usually score 2 to 3 seats in Business at schedule publish (around 12mths prior to flight) if you are lucky and get in quick enough however other than that award space is extremely difficult to come by.
If you must travel on a specific flight then your best option would probably be using cash to purchase an Economy class airfare and then requesting an upgrade using QF points. QF will then process point upgrade requests around 24hrs prior to flight departure based on Oneworld status and flight loads in Business Class. So dependant on the number of Business class seats available and your status this could approved, or declined. In addition they also have the Bid process for upgrades which is emailed out to select customers however these are processed after classic upgrade requests. In any case all of the above is a risk and you may be ‘stuck’ with your economy class seat if there are minimal or no Business class seats available.