Final answer:
The rarest animal in 'The Story of Doctor Dolittle' described as having two heads and no tail is the Pushmi-Pullyu.
Step-by-step explanation:
In "The Story of Doctor Dolittle," the rarest animal of all, described as having no tail, but a head at each end, is the Pushmi-Pullyu. This fictional creature is one of the many whimsical animals created by author Hugh Lofting. It stands out in literature for its unique appearance and is an integral character in the Doctor Dolittle series. Unlike the other options provided, which are from different literary works, the Pushmi-Pullyu is specific to Doctor Dolittle's world.