Yes it's pretty tough. Unless you want to take a risk and instruct then Cairns is pretty much out of the picture. You may get a start with a Cairns based company but you'll probably spend time in Horn Island.
Pastoralists often require a pilot but you'll also be working as a station hand too.
Look at Mt Isa, Burketown and maybe Normanton/Karumba.
I haven't flown up there for years but there's a start.
Chances are you'll be flying a C206 or C210 and living in a town that no one's heard of.