I recently made 2 five-hour trips with a pair of bunnies. I had them in a cage together. I put down a puppy pee pad, 2 cups of wood pellets, and hay to cover the pee pad. I’ve made many trips with various bunnies, and in my experience, they don’t eat or drink while in the car. Once I get to my destination, and they are otu of the travel cage, they do eat and drink. Dehydration is a concern while traveling. But My bunnies don’t drink every hour while at home anyway They drink mornign and evening. During the day they sleep. They don’t eat or drink between 10am and 5pm. So honestly – I think yoru bunny will be fine without food or water int he carrier. I would do the pee pad and hay, because your bunny might pee. And although they don’t necessariy eat during the day, they do nibble on hay if they are stressed or angry – and a car ride will do that.
When you get home, and your bunny is set up in it’s new home, provide food and water as normal. Don’t be concerned if bunny doensn’t eat/drink immediately. They need to feel safe before they eat/drink. A car ride, and a new surrounding won’t do that. After bunny has explored the new home, it will eat/drink.