Animals should only be able to teleport if given an Ender pearl

We’ve all been there. You get a dog or a cat for some companionship, go out for an adventure, and in the middle of it BAM, your dog appears in front of you and gets hit by your sword. Or even worse you are a responsible owner, but that means that you have to leave him sitting in the house all of the time. Don’t you wish that much like a real pet, you could let your cats and dogs roam around without teleporting right to you? 

For this reason, I am proposing that teleporting pets only be able to teleport if first given an ender pearl. The basic idea of this is that once a cat or dog is right clicked with an ender pearl, it can teleport for an unlimited amount of uses to its owner. Then, if the player wishes for the pet not to teleport, they can remove the pearl using a tool like shears (because right click already has a function). 

While I am unsure how this could be visually cued to the player for cats, I believe that for dogs, this would be indicated via a pearl that the collar goes through on dogs that can teleport.