Heat a small amount of cooking oil in a frying pan and add the diced onion. Sauté until translucent. Add the diced carrot and chicken, sauté until the chicken turns white and the carrot becomes tender. Add the green peas and continue to sauté for about 1 minute. Add the cooked white rice and stir-fry until evenly mixed. Add the tomato ketchup, salt, and black pepper. Stir well to combine all ingredients. Transfer the fried rice to a plate and set aside.