Robert Munsch first told this version of the story in 1987 in Geraldton, Ontario, where some of the cars that came for his show had dead moose on them. He kept telling it all through Northern Ontario, where he was on tour. It became one of his favourite stories to tell, and it had LOTS of different versions.
There was an Inuit version where the animal is a caribou. There was a Northern Ontario version where the animal is a moose and the kid wants to keep it for a pet, a Toronto version where the animal is a raccoon and the kid calls the police, a Texas version where the animal is an armadillo, and a Prairies version where the animal is a buffalo.
Finally, Munsch's publisher wanted to make the story into a book. But the story had no kid! Luckily he remembered a kid named Luke who had sent him a wonderful letter about his "tree house," which was strangely not in a tree. Munsch made up a brand new version of the Moose story for Luke and his family.