The Bible forbids the eating of pork but I've never come across anything relating to dog or cat either (lapin de toit) for that matter.
Dog and man are symbiotic creatures which are beneficial to one another's survival as species. I don't think dog should be at the top of anyone's menu. That said, if things get tough, protein is protein.
Maybe God was smart enough where he felt he provided enough intelligence for people which would allow them to readily recognize a dog’s intelligence, loyalty and contributions to civilized people.