From a literary history story on lithub.com headlined “Beatrix Potter, tired of rejection, self-publishes her first book, The Tale of Peter Rabbit”:

On December 16th, 1901, 35-year-old Beatrix Potter printed 250 copies of a book that she had written and illustrated herself—a book about a mischievous bunny named Peter Rabbit. Potter had originally written the story for the five-year-old son of her former governess, who suggested that Potter’s drawings and stories might be turned into books for all children.