Rinse the turkey and pat very dry with paper towels. Drizzle the bottom of the turkey with olive oil and half the garlic salt and onion powder. Place the turkey in a disposable roasting pan fitted with a wire rack.
Put the quartered onion, apple, carrot and celery in the cavity along with the bay leaf, garlic clove and peppercorns. Drizzle the top of the turkey with the remaining olive oil and the remaining spices. Tie the drumsticks together and tuck the wingtips under the breasts.
Smoke at 225 degrees F for 30 minutes per pound until a thermometer reads 165 degrees F in the thickest part of the thigh and 155 degrees F in the breast. Remove from the smoker and cover in foil. Let rest for 15-20 minutes, then carve and serve.