Its pretty warm in Darwin all year round but Nov-Mar is commonly referred to as the wet season in the top end and about 80-90% of the yearly rainfall falls during these months. It will be pretty hot (ave daily temps around 30C) and sticky and it won't cool down much at night in the northern areas. To be honest it's probably not the best time of year to go touring but if I had to fit two months in during this period I would probably start from Perth in Nov. I think this will give you a tail wind (though not positive), some nice riding temperatures to start with and it will be relatively dry in the WA section.
June to August would be a better time of year to do some riding in this part of the world...