While there is no dietary requirement for carbohydrates in a dog's diet, carbs and fiber can provide energy and keep the gastrointestinal tract healthy, according to Merck. Step 1. Cook vegetables for your dog. Summer or winter squash, green beans, peas and white or sweet potatoes are all good sources of fiber.owever, if you want to add fiber to a raw or home-cooked diet, grains add both carbohydrates and fiber. Step 4. Mix some wheat bran into your dog's food. Bran is very high in fiber, so just use a sprinkle at first.