Hi,
Well, the quickest way would be fly... there's an airport near there. I am not sure if it is accessible via the cheaper flights in Autralia though.....
On the other hand, it might be cheaper to bus it, but it's quite a ride from Sydney. Can you change your ticket to fly into Brisbane and then bus it (shaves a good 15 hours off your bus ride...). Greyhound/Mc Cafferty's are then the fastest but it's still quite a sit from Brisbane (good 24 hours if I am not mistaken - sorry, it's been a few years since I did that trip :) ).
HTH! Sam
ps. even if you're on your own, I would recommend quite a few of the stops on the route Sydney-Airlie... Byron Bay and Fraser Island to name a couple....