Check out http://www.greekferries.gr/pets.htm
You can also book online at this web site.
I don't think any ferry company allows dogs to remain in your car or
campervan. I took Minoan recently and they have a "dog's village" on the top deck both ferries I used. However my dog got too upset in the village and I
had to release him and keep him with me. He escaped a couple of times and
ran all over the place causing a certain amount of havoc :)
Dogs are strictly speaking not allowed inside but I managed to keep mine
hidden for an hour or so before he was sussed. They can apparently be
smuggled into a cabin if you are discreet and the dog doesn't bark.
If you plan to save money by not taking a cabin it is essential to remember
to bring a blow-up bed or lilo, sleeping bag and pillow so you can sleep on
deck or inside. The floors are very hard and most seats are snapped up
very quickly by foot passengers.
You may also be interested in leaving your car or campervan at home and
taking the dog by train and ferry.