The bunnies become targetable and "catchable" only specifically on April Fools Day of each year. There are titles earned for catching more and more of them, but they serve no function other than on that one day.
That hasn't always been true. https://forums.daybreakgames.com/eq...-is-a-silly-place-with-killer-rabbits.564313/
That's hilarious! I was gone from the game back in 2015 so I don't know if they ever did anything different at any point, but April 1st has always been the only day I've ever known the bunnies to have any interactivity in this game.