THINGS I DID NOT KNOW! The Kryptonite Man first appeared as the Kryptonite Kid in Superboy #83, and not as a full-grown enemy until Superman #299 in 1976! And in his first appearance, he had a like-powered bulldog called Dogito! (Yeah, I'm not a big fan of that name.)
Superboy first meets him in a series of dreams, where he taunts the Teen of Steel nightly. When Krypto comes home, he too suffers from these dreams, which include a kryptonite dog. The next day, the two Kryptonians are helping the town build a playground when they're approached by K-Kid and Dogito, who are turning everything they touch into deadly kryptonite. Just another dream? Fair question in the Silver Age, but no. This is real. And even hiding in a lead pipe isn't going to save our heroes.
The Kryptonite Kid AND Dogito will be back though...
BONUS! Puppy Krypto is in the third story of this same issue, "The Invasion of Krypton". These flashbacks to Kal-El's early childhood can be a little upsetting because he plays way too dangerously with his pup.