Here's a possibility I found, by searching Google books for the terms Spaceship + Koala.
It gave a few very brief snippets that made it seem like a possibility. THen a Google search found this article.
The Star Dummy - Anthony Boucher (1952)
Paul Peters is a small-time ventriloquist ...
Seeking relaxation, Paul takes himself off to the zoo. Sadly,
relaxation was not to be had that day as the zoo is atwitter. It seems
there’s a strange beast in one of the cages, described simply as “like
a koala, except where it’s like an anteater.” Ever intrigued, Paul
makes his way to the scene of the mystery and finds a small furry
creature not entirely unlike a koala drawing diagrams of the solar
system in the dirt. ...
Paul convinces the zoo staff that the whole thing is just one big
publicity stunt. The two exit the zoo ...
Mr. Koala isn’t here to harvest the world’s supply of eucalyptus
leaves, but merely searching for his girlfriend who was lost on the
planet a few weeks before ... the two decide to form a ventriloquism
act, get themselves on television and thus publicize themselves so
that Ms. Koala can find them ...
Not bad for a story, that interestingly, is all of 12 pages long.