We are animal lovers and we have 2 small dogs that we normally take everywhere we go. The cat can stay with family, but generally, if the dogs don't go, neither do we.
For the most part I've seen "No Pets" on rental sites... is that going to be all I see?
Has anyone taken their own animals out with them? Is it maybe not such a good idea anyway?
Neither of my dogs are great with water, but they aren't good with strangers either, which worries me when thinking of boarding them.

Many houseboaters take their dogs with them on their private boats. Regarding rentals, I would suggests you contact the individual rental agency to find out. They may allow, but charge additional

Thats a good point. Thanks.

I have a dog that I always take on-board, but if I was hiring out a vessel I would not allow pets. I would be concerned that a subsequent hirer may have some sort of allergic reaction to pet hair, etc.

I've allowed house tenants to have a pet, but they had to have all the carpets and curtains cleaned as part of the "pet lease". Since a house lease is a lot longer than a boat rental, the extra effort is warranted.

A good boarding kennel will have experience with handling dogs that are not used to separation from their owners.

If you are really concerned, you could try leaving the dogs for a few days and see how they react.

I googled "pet houseboat rental" (leave off the quotes) and got a number of rental companies that allow pets, in many different areas of the country. Most charge extra, but considering what most boarders charge, it equals out.