Not for a few years now, but I've flown Virgin Cairns to Perth about a half dozen times with one board and two sails. At the time Jetstar couldn't take gear but Qantas could, things might be different now. Get on the web sites and make a couple of calls.
I have family and friends in WA so transport and Accommodation were easy. I did drive once but I was on long service so plenty of time, if you have the time that's the go