I haven't had small pets since I was a kid, but I definitely would not leave an animal alone in a tent.

In our area I wouldn't worry about predators so much as simple heat. Raccoons and coyotes aren't likely to bother a tent in the daytime when you're not there, predatory birds and snakes wouldn't be able to get into a tightly zipped space. But it gets very hot inside a tent in the summer.