Definitely definitely take your car.
First of all, its a fantastic drive from SE Australia to the Kimberley.
You will go crazy not being able to drive. Broome is do-able on a bike, or a scooter, but the wet season makes life difficult. And the ability to just pack the car and drive with everything you have, to Kununurra, or Exmouth, or Darwin for that new job - that ability is priceless.