Many players carry small animals in their inventory, so why not make it an official mechanic?
Small animals and insects could be designated as pets by right clicking on them and selecting the new option "make a pet". The animal would then follow the player around when not stored in the player's inventory or a container. Killing or stealing someone's pet would count as crimes and would only be possible if the owner was KO'd or killed. Cages could be implemented to display pets inside a house. There should probably be a maximum of one pet per person to avoid trolls intentionally lagging others to death with an army of animals. Chickens and rabbits could become pets but would lose the ability to breed or produce eggs.
Sorry if this was already suggested. I could've sworn this had been posted before, but I searched and found nothing.