Well I wouldn't call my dog a "vegan" as she doesn't base her consumption choices on ethics so much as appetite
She probably eats a healthier diet than we do! She gets steamed vegies for dinner, fruit for breakfast (loves bananas, grapes, apples, pineapple), muesli, raw nuts (very occassionally) and bread as a snack. She also loves the biopet vegan dog biscuits. Sometimes we'll give her those with a bit of peanut butter and she goes nuts for it! She'll get a bowl of Veganpet dog food maybe every second day which meets all the nutritional requirements. Plus we will supplement her diet with flaxseed and savoury yeast when we're low on Veganpet.
That's what we feed her, but we can't and don't stop her from eating whatever she wants so long as we know it is safe. Anyone who's walked a cute little dog past a busy al fresco cafe will know how hard it is to do that
Domestic dog breeds evolved alongside humans and their digestive system is very similar to ours as they have been eating whatever scraps humans gave them for millenia. They are omnivores, just like us. If humans can survive on a vegan diet (and we know they can), so can dogs.
Cats are another story, however, but I know of many cats who have thrived on a "vegan" diet for years.