If you have Barnacle Bay, here's an answer I gave on another thread. Also, you can use the collection helper to find the small pets.
Did a quick trial this morning in Barnacle Bay with the collection helper. There are spawn points for all the minor pets. I've only looked at the end of the first day, so I'm guessing more will pop up over a few game days. I have to go out now and can't keep looking, but I'll look more when I get back.
For now, near the military base and cemetery for snakes. Near the school for turtles. Rodents behind the tattoo salon. Lizards on the other side of the road where the cemetery is. Seems to be a few for birds already - At Grace's Garden, on the beach opposite the art gallery and near the house up near the Garden of the Forgotten.