Tamed Rabbits will not teleport to the player(as far as i know) unless the player is next to a liquid(Lave,Water). I ran around a cave and i and had just tamed a rabbit a few minnutes before, and he only seemed teleport when i was near cave water, and then i ran past some lae and heard aqeeak and he was deam as hell. 😞
I believe this is a duplicate of MC-55661. MC-55661 is very confusing because it causes people to think that animals simply won't teleport, but in fact they do, it's just using bad criteria.