So ive looked up on other forums about pets. They are summoned from items that can be found underground in chest, or on floating islands. These are the ones you can get:
Cabbage: Summons a Guinea Pig
Paintre Dish ( pretty much a plate): Summons a Slime
Brain: Summons a Zombie
Vial of Blood: Summons a Bat
Those are the ones I remember, ill make another post after I check on the others.