Have you tried May 23?

This has a somewhat decent connect via MEL
Have you tried May 26?
Now look I know routing yourself via CBR and MEL is less than ideal. But there is availability then on QF metal for the price you're after!
Couple of other thoughts here. One thing you can try off that bat is looking for Premium Economy classic awards. I understand that's not what you want, but it'll get you a ticket booked in the routing you want with QF, as Premium Economy classic awards are easier to come by. From there you can request an upgrade into business class using points which will likely clear around time of departure if there is any availability. I know you're really rolling the dice here, but at least you'll have a ticket in hand, and I can tell you from experience that sometimes extra space is released for upgrades as you get closer to departure when QF realizes they won't be filling that J cabin. That happened to me on my flight a couple of months ago from BNE down to SYD.
Second option is to be patient and flexible. By patient I mean don't expect that you'll find the availability today or tomorrow or even next week. Keep looking from time to time and you might surprise yourself what you'll find. Remember you've got nearly a year to book the darn thing, and frankly it won't matter if you book it right this moment or in a month or two's time. You also need to be flexible on your departure with business awards. In other words, if you see a business classic award that roughly suits your schedule, book it now and ask questions later. These tickets are elusive for a reason! Remember folks are paying $8000 or more return to have the honour of flying J be it on QF, AA or UA.
One other consideration - how loyal are you to Qantas? Do you have points with other programs like Virgin Australia or British Airways? Do you have transferable points on credit cards like American Express which can be sent to many frequent flyer programs in a flash? The reason I ask this is that sometimes Qantas isn't the best redemption. Case in point, I'm flying from Sydney to Saint John on the east coast of Canada, all in business class on Air Canada and I redeemed 80,000 points for that (which I bought when AC was selling points at about a penny a point).
-RooFlyer88
-RooFlyer88