We were genuinely concerned how the dog would fare because he is excessively overly attached to my husband. He flips out if the man walks out the door without him and cries, whines for hours.
On the 4/5 hour drive to the pier, he stood the entire way in the back seat. We spent the night in a hotel, dropped the luggage at the pier and took the dog to a local doggie beach to wear him out. That morning, the dog had busted out of the hotel room, ran down the hall and found my husband in the breakfast room. My son buckled him into the back seat (for those who don't know, there is an attachment that hooks to the safety belt and then hooks to the dog's collar where you can control how much play the leash has or how far they can roam). We talked to our son from the ship about an hour later and the dog was still crying during the long ride home.
That said, he finally fell asleep exhausted and although picky eating a few days, he was FINE. 15 days later upon our return, he was excited but picked right back up on his normal routine and did not go back into his severe separation anxiety we feared would return.
So no matter how much you think they can't live without you, they will survive - take your cruise and don't worry about your furry friends - they will be fine!