The story is actually about two rabbits, Benjamin Bunny and Peter Rabbit. Benjamin, being much braver than Peter, is shown to be a more resourceful rabbit when it comes to finding food and avoiding danger. The story emphasizes the importance of being cautious and resourceful, especially in the face of danger.
It's possible that you are thinking of a poem that references cottontail rabbits, but isn't written by Beatrix Potter. There are many poems about rabbits, but without more information, it's impossible to know which one you're looking for.
Do you remember any other details about the poem, such as its theme or any specific lines? Knowing more could help me identify it!