Add the carrot, celery, onion, and garlic to the sausage. Stir to combine and cook the veggies for about 5 minutes. Add the oregano, rosemary, salt, wild rice, stock, and water to the pot. Stir everything together and cover the pot. Reduce the heat to low and let the soup simmer for about an hour, checking it every 20 minutes, until the rice is cooked through and tender. Each time you stir the soup, taste the broth and add a few pinches of salt as needed.