Remove giblets and neck from duckling; reserve for other uses. Rinse duckling thoroughly with cold water, and pat dry. Prick fatty areas of duckling with a fork at intervals. (Do not prick breast.) Lift wingtips up and over back, tucking under duckling securely.
Combine salt and pepper; sprinkle over surface and in cavity of duckling. Stuff cavity with celery, apple, and onion. Close cavity with skewers, and truss. Fold neck skin under, and place duckling, breast side up, on a rack in a shallow roasting pan. Bake duckling, uncovered, at 325° for 2 hours and 45 minutes or until drumsticks and thighs are easy to move. Remove duckling from oven, and discard celery, apple, and onion. Transfer duckling to serving platter.