Yes, some routes and/or days of week do have single seat available for awards. This is adjusted by yield management as they see demand, but no guarantee when additional seats become available. You would be very wise to book the QF flights 355 days ahead, when QFF inventory is released, and not 330 days ahead, when Oneworld inventory is released (and BA/AA snap up the QF awards). You may have to route via SYD (tends to have more availabilty) or even ADL/BNE/PER to hub in SIN. Be sure to pick unpopular days of the week/month is you don't care about when you travel, there is a huge difference in demand and award availability reflects that. An option is to sign up for one of the commercial availability tracking services, such as Expertflyer or KVS, though they aren't 100% accurate. Good luck.