According to the House Rabbit Society, baby bunnies must be fed with alfalfa hay with the introduction of some grass in the first 6 to 7 months. The amount of hay must be lowered down steadily compensating it with a grass only until your bunny reaches 1 year when the lone grass makes the bulk of bunnies diet.eeding rabbits can be a daunting task especially when you’re not aware as to what to feed rabbits. There is a general belief regarding rabbits diet in that the species can be fed on lettuce and carrots; yet the truth is that feeding these items to bunnies might lead to the death.