That can be arranged. There’s a website “marryyoourpet” or some such. But they aren’t legally binding. I’m sure you remember the German postal worker who married his cat. But I don’t think it was legally binding. And they couldn’t get a clergy person to perform the ceremony so got an actress.
Given the way things are going with 0bama Care, you local vet could take care of you and your pet AND perform necessary ceremonies.