If your dog does consume smoked brisket, you should consult with your veterinarian about its safe consumption for the pet. While smoked brisket contains sodium, it is not toxic to dogs in small amounts. Large quantities can destroy red blood cells in dogs. Treatment will involve flushing the stomach or induced vomiting. A dog with onion poisoning will likely need to be under medical observation for at least a few days, and if you notice any signs of dehydration, you should seek immediate medical attention.