The puppies were born this morning.
The puppy that was standing at the entrance was given the nine balls around its neck by the prince.
Let’s pretend we’re puppies!
A child dog is a puppy!
Even though this is a jukugo word, it doesn't use the on'yomi readings. Both the kanji 子 and 犬 often favor kun'yomi readings, and this word is no exception. The reading for 犬 is the one you already know, and the reading for 子 as こ is a really common one (perhaps you've already learned that reading?). If not, just think about punching a puppy in the face, and giving it a KO (That's a knock out).