Rabbits

Rabbits come in both sexes, Male and Female.

Sources

Rabbits can be found in grass by dropping Carrots on the ground nearby.
They can also be bred in a Rabbit Hutch if you have both a male and female rabbit.

Rabbits can be found in grass by dropping multiple Carrots on the ground nearby. Carrots may randomly be replaced by white rabbits. If a spawn occurs, it will happen all at once - every carrot in visual range has a chance to change to a rabbit, all at the same time. You will have a very brief time to pick up the rabbit before it disappears, along with your carrot.

Rabbits can be caught day or night. Every 5–90 minutes (random each time), every stack of carrots in Egypt that is on grass is evaluated for a chance to be replaced by a rabbit. Thus rabbits may be caught within minutes of placing carrots, or they may not spawn before the sweeper cleans up the carrots.

A rabbit will stay for 30 seconds per carrot in the stack it replaces before disappearing. The larger the stack, the longer you have to pick them up.

More male rabbits appear to spawn than female rabbits, generally, but both are possible in the same spawn. The gender of the avatar does not appear to have an effect on the ratio of male rabbits to female rabbits.

Rabbits have been seen to appear even when the player is standing in the middle of a grid (e.g. 25 carrots over 5x5 coords), so the idea that you need to "back off" from them is not true. Rabbit spawning is not negatively affected by doing chores such as gathering grass, or by chatting with players.

Rabbits can spawn from a placed grid multiple times. If you have carrots out and a spawn wave occurs, transforming some of the carrots to rabbits, it is completely possible a second spawn wave will occur later, transforming some of the remaining carrots. You do not have to pick up and re-place carrots for another spawn to occur.

Rabbits can be bred in a Rabbit Hutch, which can hold up to 100K Rabbit Food (made from Carrots or Cabbage) for them to eat.

They may be slaughtered in a hutch for Rabbit Meat, the chance for a Rabbit Pelt and the chance for Animal Bones. Dexterity increases the chance to get a pelt and bones.

Rabbits can sometimes breed quickly. The more rabbits there are in the hutch, the more likely they are to all escape the hutch from overcrowding. They will also escape if there is no food. How much is "too much" is still unknown, but it seems that 25 or less is safe, although at that size they could easily and quickly breed to overcrowding.
Breeding rabbits eat a lot. When placed in single-sex hutches, rabbits eat very little. Up to 100 rabbits of the same sex will happily live in the same hutch without being overcrowded.