Combine 1 cup flour, 1 tablespoon plus 1 teaspoon salt, paprika, and red pepper, mixing well; dredge rabbit in flour mixture, coating well.
Heat bacon drippings in a large skillet; add rabbit, and brown quickly on all sides. Reduce heat; cook, uncovered, 40 to 45 minutes or until rabbit is tender and golden brown, turning occasionally. Drain well.
Pour off drippings, reserving 1/4 cup drippings in skillet. Add remaining 1/4 cup flour; stir until smooth. Cook over low heat 2 minutes, stirring constantly. Add milk; cook over medium heat, stirring constantly, 1 minute or until thickened and bubbly. Stir in remaining salt and pepper. Serve gravy with rabbit. Garnish with parsley.