Come a bit earlier, clear in at Cairns, do a leisurely cruise
up the coast day sailing
. pass through Albany passage anchoring
at Turtle Bay, slip around the Cape to Seisia, pass over the shoals W of crab island - there is plenty of water
for small boats, across to Gove then another leisurely coastal cruise
Do not believe all the horror stories you hear, I have been cruising the eastern, northern and western Australian coasts since 2002 and other than coast watch flyovers have yet to be even approached by any authorities.
I have a set of the 800 series charts
for pretty well all the sections of coast I cruise but seldom pull them out anymore as I have found the CM93 charts
I use with Opencpn
to be accurate enough.
Stay out of the recommended shipping lanes as much as possible, the things that use them are monstrous and travel like bats out of hell, in the close waters they don't need you getting in their way and you don't need close shave experiences with them.