Do you know why dead baby jokes are always funny?
They never get old.
Oh, boy, here we go. So, the joke is funny because it uses the phrase "never get old" in a dark way. Usually, when something "never gets old", it means it's always enjoyable. But, in this case, it's saying dead babies literally never get old because they're dead. You probably are older than some babies now. Boom! Roasted!