Given you are booking the flight so close-in to departure, your best bet would be choosing a flight that has the most business class availability now. Put differently, you want flights where there is plenty of J, C, D and (ideally) I inventory available. This would indicate that not only are there plenty of seats on the plane, but revenue management at Qantas believes they won't be able to fill all of them, and hence they'll likely offer more seats for upgrades since it's better to have a filled seat with points/cash than to send it out empty. Also, you may want to consider booking Premium Economy if you can swing it for three reasons. First, it requires substantially fewer points to upgrade. Second, it puts you higher in the pecking order. Third, you'll end more status credits which may be enough in time to make you a World Platinum member. Another factor is First class availability which I know sounds weird but hear me out. Many folks will buy a business class ticket hoping they can use points to upgrade to First class. Well what happens to those business class seats when their upgrade succeeds?
Also keep in mind that you need to book a ticket that permits upgrades. Some sale fares prevent that and it will be clearly indicated during booking (i.e. avoid the E,N, O and Q fares when booking an economy fare). To my knowledge, all Premium Economy tickets are eligible for upgrades to business.
In terms of best bets, I would say QF 12 (LAX > SYD ) on the 15th is your best bet and a look at the available fares for that flight tells us why:
F3 A3 P0 J9 C9 D6 I0 U0 W9 R9 T0 Z0 Y9 B9 H9 K9 M9 L9 V9 S9 N9 Q9 O9 G0 X9 E0
F3, A3, P0 means there are 3 seats still available as a full fare First class ticket (F) or as a First class ticket (A), although no discounted first class (P0). This means that there is still a good chance some in business could get pushed up to First class potentially freeing up as many as 3 seats in business. J9, C9, D6, I0 means 9 or more seats are available in full priced business class (J9), 9 or more seats are available in business class (C9), D6 indicates 6 seats are available in discount business, and lastly I0 means 0 seats are presently available in deep discount business class. Note: These figures aren't coughulative. So F3,A3,P0 would mean a total of 3 seats in First class, those seats being able to be sold either as Full fare First class ticket (F) or a regular First class ticket. Also, U0 means there is no classic business award availability for that flight.
To finish off the alphabet soup: W9, R9, T0, Z0 indicates there are 9 or more seats available in Premium Economy. 9 or more can be sold as a full fare Premium Economy Ticket (W9), 9 or more could also be sold as a normal Premium Economy Ticket (R9), T0 indicates 0 of those seats can be sold as a discounted premium economy ticket, and Z0 indicates that 0 of the Premium Economy seats are available as a classic award.
Y9, B9, H9, K9, M9, L9, V9, S9, N9, Q9, O9, G0, X9, E0 indicates the following. There are 9 or more seats available for economy. 9 or more of which could be sold as a Flexible economy ticket (Y9, B9, H9), 9 or more of which can be sold as a regular Economy ticket (K9, M9, L9, V9, S9). 9 or more of which can also be sold as a discount economy fare (N9, O9, Q9), 9 or more of which can be offered as a classic economy award (X9), 0 of which can be sold as a deep discount economy (E0, G0).
Hope that helps.
-RooFlyer88