Deer are very skittish, and will flee from any player that gets within 7-20 blocks away from them. Otherwise, they act similarly to most other passive mobs, aimlessly wandering around, avoiding any natural hazards such as lava, and running around in a panicked manner upon taking damage. As well as this, when undisturbed, they will occasionally stop moving and lower their head to graze on grass, converting it into dirt.
Deer can be bred with wheat or carrots, and are bred in the same manner as other vanilla animals (right-clicking with the breeding item). As well as this, they will follow any player holding an apple, golden apple, carrot, golden carrot, or carrot on a stick within a radius of 8 blocks; this is one of the only times they will not flee from a player.
It takes 1 day for a fawn to reach adulthood.