Rabbit is extremely busy and very Important. He is often in a rush to get somewhere, or do something, or see a Pooh about a Piglet.
One reason for Rabbit's general busyness might be the extraordinarily large number of friends-and-relations that he has. According to the chapter In which Kanga and Baby Roo come to the forest, and Piglet has a bath, Rabbit may have as many as 16 separate friends-and-relations, which would keep anyone occupied for quite a considerable time.
Rabbit's friends-and-relations include Alexander Beetle (Small), who stars in his own chapter of book two when he goes missing and a search is organdized for him.
We first meet Rabbit in chapter two of the first Pooh book, In which Pooh goes visiting and gets into a tight place, when Pooh gets stuck in Rabbit's front door. Interestingly, Rabbit only appears in one chapter title, In which Rabbit has a busy day, and we learn what Christopher Robin does in the mornings.