The first appearance of the character Peter Rabbit was not in a book, but in a letter! A wonderfully illustrated hand-written letter that survives to this day.
In September of 1893, at 26 years of age, Beatrix Potter sent the following illustrated letter to Noel, the five-year-old son of her friend and former governess, Annie Moore. The letter contained a tale of four rabbits, and in fact featured the first ever appearance of Peter Rabbit; however it wasn't until 1901, eight years later, that Potter decided to revisit her letter to Noel and develop the idea.
The resulting story, The Tale of Peter Rabbit, was published in 1902 by Frederick Warne & Co, and has since become one of the most popular children's books of all time.
See the original with drawings, and read the full transcript at Letters of Note. Link