In the 1950s, both funny animals and sci-fi were popular comics genres...
...so, it was inevitable that someone would combine the two!
Though it's the cover-featured story in Avon's Space Mouse #1 (1954), "Beauty Contest" is not the origin of the Rocketing Rodent.
That tale, "Atomic Attack", comes later in the book.
Artist Frank Carin began his career as a movie cartoon animator before turning to comics at Timely (later Marvel), in the late 1940s, doing the teen humor comics Georgie and Nellie the Nurse as well as the funny animal books Mighty Mouse and Wonder Duck.
He was also mentioned (along with a self-portrait) in Stan Lee's long OOP Secrets of the Comics book as shown HERE.
This led him to Avon, where he became a mainstay of their unjustly-obscure funny animal line, doing Peter Rabbit, Little Jack Frost, and Merry Mouse along with Space Mouse.
As for who wrote "Beauty Contest"...well that person's name is lost to the mists of time.
Since it's stated in Secrets of the Comics that Carin preferred to just draw, it's a fair bet he didn't write the tale.