Pets in this game are not really pets but more like familiars. They are semi intelligent summoned creatures bound to a specific item. You could try to adopt a kikiri or rat or whatnot. There is no functionality for it, of course, but if you role play it well enough at least some of the other players will spare its life when you are around. Then again you can always have an imaginary pet, purely role played that goes around with you but people might not notice it if you do not constantly mention it.