To cause the egg to teleport, press attack while in Survival or Adventure mode (press use in Creative). It teleports to an air block nearby (up to seven blocks vertically and fifteen blocks horizontally), creating the same particles as endermen. It may teleport into the air and subsequently fall to the ground since they forcefully obey gravity. If all available air blocks are filled, it is possible to break the block.
Dragon egg teleportation is completely silent.
It will be somewhere close, but maybe in a cave under where it was when clicked