It’s not impossible to find, but you will be up against it. I wouldn’t take too much from searching January this year, because there likely were a handful of seats to begin with but because it’s such a peak demand and those seats would have been on sale in February, it’s no surprise if you wouldn’t find anything left at this stage.
There is a chance you will find award seats, however you will have to be very organised. Flights are released to frequent flyers 350 days in advance through Qantas, and I think slightly later like 11 months maybe, for JAL if you’re searching through the Qantas site. Asia miles I couldn’t tell you for sure as I don’t partake, but I’m 99% sure it’s something similar in that it will be about 11 months prior. Because it’s such a peak season for travel and the demand for the seats is there, once the initial offering of award seats get snapped up I find it highly unlikely any more seats will drop in later - the demand is there and Qantas would rather sell those seats for cash.
The biggest issue I can think of is you say a family trip - how many seats are you after? In my experience award seats are often released in pairs, so if you’re after two seats I’d give you half a chance if you’re flexible in dates and open to the via Brisbane and Melbourne flights, but getting a family of say 5 all award seats on the same flights during peak season will be really tough for you.
The key to get what you’re looking for is going to be getting organised and being a little flexible. If you have a little flexibility in dates and you’re open to all options (Qantas via MEL/BNE/SYD, JAL direct, Jetstar via Cairns etc.) that will give you the best possible chance of finding what you want when the time comes and they go on sale.