Forget the Perth way unless you are looking for a looong cruise
. Without doing the maths, it has to be 5 or 6 times longer in distance, crosses several climate zones (all twice) and includes at least 1,500 nm along the top of the Southern Ocean.
Darwin to Cairns is not that difficult. Leave early in the monsoon build up as soon as the dry season Easties start dropping out -usually October / November. Be prepared to motor
in the calms and hole up if strong Easties re-assert themselves for any length of time.
Split the trip at Gove (good anchorage) and await for a weather
window to cross the Gulf.
Again regroup at either Thursday Island or Bamaga and then make the run down the east coast
from Cape York to Cairns. There are plenty of good anchorages
inside the reef if the (now) South East trades remain in force (and thus on the nose). As the reef is close to the coast for this section, you won't have to deal with large seas if the SE trades are present but you will have to deal with 25+ kts right on the nose!
But usually the trades have dropped out by November/December on this leg.
If the monsoon is present, you will have intermittent North Westlies and calms. Of course, you run the risk of cyclones but that is not so high early in the monsoon season and these days you get enough warning (usually) to bolt for a hole.
Disclaimer - I have not personally sailed this route
but I have had my 28 Wanderer sailed (delivered) by my mate from Darwin to Brisbane
(and it did NOT go to windward). I have lived in Darwin, Cape York and Cairns for quite a few years.