In a saucepan, heat vegetable oil over medium-high heat. Add onion and red pepper; cook 4 minutes. Transfer to a bowl.
Return pan to heat, and add ground turkey, garlic, chili powder, cumin, and salt. Cook, breaking up meat with a spoon, until cooked through, about 4 minutes. Stir in diced tomatoes, kidney beans, carrots, and cooked onion and pepper. Bring to a boil, reduce heat, and simmer, covered, 10 minutes.