Dogs can and do perfectly well on a vegetarian diet and there are veggie diets out there for dogs.
People get confused with the word carnivore. The dictionary definition is different from the scientific one.
Everything about a dog tells you it is a carnivore, the fact that it is omnivorous does not change this.
For example, cows and sheep have been eating processed foods made up of dead chickens etc, does this make them carnivores?
My horse used to eat a ham sandwich, did not make him an omnivore or a carnivore!
No they are herbivores.
The problem with feeding a vegetarian diet is that dogs require ten essential amino acids they cannot synthesise for themselves so it is necessary to add these.
Most vegetarian diets get round this by including soya however soya is a very unsuitable food for dogs as it is a goitrogen and it is a prime producer of GAS!