Bear in mind, Kamandi was raised in the bunker by his grandfather (no information about Kamandi's parents was ever disclosed) and it was vaguely implied that said grandfather was born before the Great Disaster. (A retcon by subsequent writers established that Kamandi's grandfather was none other than OMAC -- the Kirby hero, that is, not the DC android villains -- but that was later.) So not that much time passes between the fall of humanity and Kamandi's era: merely two generations. There are also references to the animals having access to some old books and recordings of man's time which they imitate, even if they misunderstand a lot of what they've seen.
Also, Dr. Canus knows more than the rest about the past human civilization, so he could easily have told Caesar what a warhead was called. (And certainly chose not to tell him what it could do.)