Sprinkle gelatin over 1/2 cup cold water in a small saucepan; let stand 1 minute.
Cook over low heat, stirring until gelatin dissolves, about 2 minutes.
Combine gelatin mixture, yogurt, and remaining ingredients in container of an electric blender; cover and process until mixture is smooth, stopping once to scrape down sides.
Pour mixture into freezer can of a 2-quart hand-turned or electric freezer.
Freeze according to manufacturer's instructions.
Let ripen 1 hour, if desired.
Scoop frozen yogurt into individual dessert bowls.