I believe this was my once long-lost book as well. I found it while looking for an answer to another question on this site. I can't really confirm the details as it's been forever since I read it from my elementary school library. I would love to find an affordable copy.
"The Rock of Three Planets" by A. M. Lightner, published in 1963. It is apparently the first book in a series. (?!)
In the twenty-second century, young Johnny and his friends are preparing [not] for a dog or pet show, but for an Extraterrestial Animal Show. With the weird ""rock"" as his entree, Johnny walks away with the Best In Space ribbon to the amazement of all the other contestants. Subsequently, Johnny, Cherry and Uncle Rob set off on an X-Tee expedition. Strange things happen after a spaceship-wreck lands the three on an odd planet, but in the end, the incomprehensible becomes comprehensible.