It's Not Covered in the Zombie Survival Guide

Ash and I are watching the utterly abominable remake of Dawn of the Dead. Honestly, I don't know why we haven't turned it off. It's really horrible and clichéd. Anyway, I've got to thinking:

Strictly speaking, wouldn't zombie dogs eat other non-zombie dogs, not necessarily people? I mean, in the movie, the zombie people ignore the non-zombie dog, and if it were simply a matter of needing flesh or brains or whatever for survival, surely the zombie would grab whatever living flesh comes in range. This leads me to the conclusion that zombies must be limited to flesh of their own originating species. So wouldn't zombie dogs have to eat non-zombie dogs?