If you decide to explore on your own using a rental car, I recommend renting one in Adelaide but try and avoid driving at dawn, dusk, or nighttime as wildlife is prolific and a collision with a kangaroo can be very expensive, not to mention destructive. While you don't need a 4WD for the main roads, many of the roads are unsealed, so consider renting an SUV. Check your contract to see if your car-hire company allows their cars to be driven on dirt roads.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.