Preheat oven to 400 degrees F. Line 12 muffin cups with paper liners. Combine rice flour, baking powder, and salt in a medium bowl and set aside. In a separate bowl, beat the butter and 6 tablespoons sugar with a mixer until light and fluffy, about 3 minutes. Add eggs, beating well after each addition. Mix in vanilla extract, then add flour mixture alternately with milk until just blended.
Divide batter among prepared liners. bake in the center of the oven 13 to 17 minutes, or until a toothpick inserted into center comes out clean. Transfer to a wire rack and let cool completely.
Combine egg whites, 1 cup sugar, corn syrup, the water, and cream of tartar in a deep bowl. Place bowl over a saucepan filled with 1 inch of simmering water. (The bowl should not touch the water.) Beat with a hand mixer for 10 minutes, so that egg whites are heated to a safe temperature. Spoon into pastry bag with a plain 1/2-inch tip and pipe onto cupcakes. Sprinkle nonpareils around the rim.