Strays aren't very common on Baisla, but yes, it is possible to find the occasional stray domestic dog or cat! The dogs tend to be sato dogs, small mutts with terrier traits. There's a wide variety of non-domestic wildlife on Baisla too. And yes, it is a bit like monkeys are to humans. As per the Setting page:

"You can hunt and eat the wildlife here, though it's not common practice; the Animalians mostly eat fish. They won't get angry with you for eating other stuff, but it is generally accepted that they don't eat the other non-sapient animals because it's sort of like a human eating a monkey. It's just weird!"