You're right, it's the worst time of year to be riding in tropical Australia.
Heat and humidity are not necessarily problems per se, but tropical cyclones, storms and floods could make the ride impossible in some places, even on the highways. However I don't know what the long-range weather forecasters are expecting the coming season to be like. Some years are worse than others.
It's true there's no railway line from Perth to Darwin. You'd have to use the Adelaide-Darwin line.
On the bright side, summer is a good time of year to be riding down south. Maybe you could delay your departure by a couple of months so that you could ride all the way to Darwin.