Sprinkle salt and pepper over quail; dredge in 1 cup flour, coating well. Heat 1/4 inch oil in a large skillet; add quail, and fry over medium heat 10 minutes or until golden brown, turning occasionally. Drain.
Pour off drippings, reserving 1/2 cup in skillet. Add remaining 1/2 cup flour to reserved drippings; cook over low heat 1 minute, stirring until smooth. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Stir in 1/2 teaspoon salt, 1/2 teaspoon pepper, and Worcestershire sauce.
Return quail to skillet with gravy; cover and simmer 1 hour. Arrange quail on a serving platter. Serve immediately with gravy.