Older baby bunnies who are found outside of the nest may not be orphaned or in need of assistance. This is most often the case. Baby cottontails are born without fur but develop a full coat in a week. Their eyes open in 10 days, and in three to four weeks they are weaned. baby of only 10 days to 21 days or so should not be found away from the nest. At that age they stay pretty close to the nest. If a nest can’t be found that means the baby is pretty far away from the nest for a reason.