Place a Dutch oven coated with cooking spray over medium-high heat until hot. Add chicken and onion; sauté for 10 minutes. Add celery, and sauté 2 minutes. Sprinkle chicken mixture with flour, and saute 1 minute. Add broth, carrot, 1/2 teaspoon thyme, and pepper, stirring well with a whisk. Cover, reduce heat, and simmer 10 minutes, stirring occasionally.
Combine 1/4 teaspoon thyme, baking mix, and milk in a small bowl. Drop the dough by tablespoonfuls onto chicken mixture. Cover and cook over medium-low heat 15 minutes or until dumplings are done (do not boil).