Alas this is relatively normal in really cold weather.
I also live in central Victoria and it's likely to be your carburettors freezing, as it happened on my ZZR600 quite regularly in winter in the Macedon Ranges. Once this occurs you lose all power, but when you pull over the problem mysteriously goes away as they defrost really quickly. FWIW my first car had the same issue, so it's not just bikes that suffer.
There's a few things you can try.
1. Run a denser fuel like the dreaded Shell Optimax (if it's still available) in winter. People normally bag this fuel, but it ran in my bike with zero issues.
2. Block off part (not all) of the radiator with a cardboard or plastic shroud. This cuts the airflow through the radiator and the engine will run a bit hotter. A few caveats with this one. Take it off in summer and on warm days and if you are in a lot of start-stop traffic.
3. I'm not sure if later models of ZZR250 came with heated inlet manifolds (my 1998 ZZR600 didn't, but the 2000 model did). If they did see if you can find one in a wrecker and replace yours. You may find that there is a hot water connection from the water pump up to the manifold, so you may need the water pump housing as well. The good thing about the ZZR250 is that it was basically the same from the beginning of the model run to the end, so you might get lucky with parts.
Anyway, good luck with it, it's a pain in the arse and it may be easier just to pull over for a few minutes and let everything thaw out. I know the plastic/cardboard approach works, although it looks odd and you have to be careful not to damage the radiator fins when attaching it. If you are worried about looks you could always paint it black

.
HTH, Mick