These harmless floppy-eared creatures wander around aimlessly. When killed, they make a squeal noise and then sometimes drop a Rabbit's Feet or a Small Heart. They have 10 health (5 hearts) so they die rather easily. They tend to destroy crops (especially carrots).
You can obtain multiple Rabbit's Feet by breeding the rabbits with carrots. Rabbit's Feet cannot be used as a food source. Currently, there is no known use for rabbit feet.
There is a glitch that causes the rabbit to sink through a block occasionally, though it jumps back up in a while. The rabbit was seen glitching on a village crop-farm structure that was spawned on water. This is very similar to the server glitch where mobs appear half-sunken into blocks.
Also, when hit by Bane of Pigs, the rabbit will not attack you, but will still do the same strange thing as other Project Zulu mobs.