You are allowed to drive your car on Ameland. But the village centres of Hollum and Nes are car free.
If you wish to bring your own car to Ameland, you will have to book a place for the crossing on the ferry in time. You can do this online at Wagenborg Passenger service, or by phone 0031-88 103 1000. If you call from the Netherlands, you can reach Wagenborg Passenger service via 0900-9238.
More information about the ferry time table, prices and departure times you can find here.