USE THE FERRY TO JUMP ACROSS ISLANDS
There's two companies that you can use to ferry across (you, your campervan and luggage) both islands.
The Interislander and the Blue Bridge.
Both are super awesome, The Interislander does 3 trips a day, the Blue Bridge does 4 - so no matter what time you want to cross (morning, arvo, late night) you'll be fine.
Book your tickets early, especially in peak season (December/January).