A pushmi-pullyu is NOT fictional. Dr. Dolittle bring one of the last pushmi-pullyu to England in the 1830s.
The pushmi-pullyu is a fictional creature from the "Doctor Dolittle" book series written by Hugh Lofting. It was never a real animal, but rather a fantastical creation for the story.
It's name was Pushmi-Pullyu
It's not a llama, as they only have one head. It's a pushmi-pullyu.