Unless you're referring to the song from Snoop Dogg's landmark 1993 album "Doggystyle," you probably mean "dog-eat-dog world." But maybe the confusion developed because dogs aren't cannibals.
The saying is actually a corruption of the Latin phrase canis caninam non est, which states that dogs do not eat each other. Nevertheless, "dog-eat-dog" is meant to convey the viciousness or "every man for himself" nature of life and society [source: Paton]. So leave out the "doggy" unless you're a die-hard Snoop Dogg (now Snoop Lion) fan and believe it's his world and we just live in it.