It is possible for dogs to have a vegetarian diet. 

Cats are true carnivores and so must have animal protein as part of their diet.

Adult cats and dogs, like some humans, lose the ability to digest lactose, the sugar found in dairy products.  Feeding cats and dogs milk usually results in diarrhea, never much fun to clean up.  There are products out their like "CatSip" and "Frosty Paws" that are formulated so that pets can consume them.

Chocolate, coffee, onions, macadamia nuts, raw potatoes, grapes, and raisins are toxic to dogs.  This also means that you should keep your pets out of coffee grounds.

You should never feed your pet artificial sweeteners such as Nutrasweet also known as aspartame (the blue packets), saccharin (the pink packets), Splenda also known as sucralose (the yellow packets), acesulfame K also known as ace K or acesulfame potassium, and sugar alcohols such as sorbitol, mannitol, isomalt, lactitol, maltitol, and xylitol.

You should never feed your pets alcohol.  They don't have capacity to metabolize it.

Also be aware that you should avoid feeding your pet the pits of apricots, cherries, peaches, or nectarines.  You should also avoid feeding your pet pear or apple seeds.

Email: info@creature-care.com