The bast way to get around Couran Cove is to hire bikes and ride - they give you a a chain and there are bike racks everywhere. There are no guest vehicles on the island and even the room-service and housekeeping staff get around on specially fitted bikes!
There is also a people-mover train thingy that goes through the middle but we only really used it to get to the restaurant one evening at the surf beach (away from the main accommodation areas) when we thought we may be a little 'unsteady' on our bikes after a night of good food and drink.
From Sydney you can catch a flight to the Gold Coast or Brisbane and then get a coach transfer to Runaway Bay to connect with the ferry crossing to the island.
We caught a Qantas flight to Gold Coast (but you can also take Virgin Blue - similar fares)