Dry the pineapple: Pat rings thoroughly dry on paper towels and let sit 5 minutes before battering.
Make the batter: Whisk flour, sugar, baking powder, cinnamon, nutmeg, and salt in a bowl. Beat egg with milk and vanilla separately, then combine with the dry ingredients. Stir until just combined - a few lumps are fine.
Heat the oil in a deep pot to 350 to 360 degrees.
Fry the fritters: Dip each pineapple ring in batter, let excess drip off, then lower carefully into the oil. Fry 2 to 3 rings at a time for 2 to 2.5 minutes per side until deep golden.
Coat and serve: Transfer to a wire rack. While still hot, toss or dust each fritter with the cinnamon sugar mixture. Serve immediately.