Short answer: Yes - but probably not.
You pay stamp duty when you transfer it into your name, so you'd need to go into a QLD government shopfront and transfer it. Show your licence etc.. If it's a WA licence and you claim you live in QLD then they will get you to transfer your licence also - game over.
In saying that - I've done it!
I live in the ACT and when I bought my 73' 911, it had NSW plates. I also managed to get the plates NIN311 (available through NSWRego for $210!) and so I wanted to keep it in NSW. A mate of mine owned a butchers shop in Sutton NSW (not far from ACT) and so I got a letter from him stating that the car was kept in his garage as it wasn't my daily drive - only a weekender (it was my daily!). SO although I had an ACT licence, the registration papers stated the car must be regestered to its garage address - not the owners.
Unless you say you keep your car over in QLD as that's where it's garaged, I don't like your chances.