We're in the same boat as you as far as trying to book an award EWR-CNS. After researching this A LOT, the best we came up with was UA Award EWR-SYD and then QF Paid SYD-CNS.
Make sure you leave a lot of time between the arrival of your UA flight and the departure of your QF flight. Being on separate airlines and separate tickets, QF probably won't show any sympathy if you miss their flight because you're UA flight was late.
For example: We arrive in SYD at 7:00am on Day 1. We won't depart for CNS until 1:00pm on Day 2. Since we have the time, we are going to check out Sydney and recover from our jet-lag there. Also, god forbid we don't get on the once daily flight to SYD, we still can be on the next day's flight and make the flight to CNS. As I said though, we are lucky to have this freedom and I realize many people will not.