Preheat the oven to 375 degrees . Grease and flour a 12-cup muffin pan.
Spread the shredded coconut on a rimmed baking sheet and toast in the oven, shaking the baking sheet occasionally, until lightly browned, about 10 minutes. Let cool.
Meanwhile, in a large bowl, sift the flour, baking powder, cinnamon, nutmeg and salt. Stir in the granulated sugar and 1 cup of the toasted coconut.
In a small bowl, stir together the coconut milk, melted butter, eggs and rum. Add to the dry ingredients and stir until just combined. pour the batter into the prepared pan, filling about three-quarters of each cup; bake until lightly golden and a toothpick inserted comes out clean, about 35 minutes. Transfer the cupcakes to a rack to cool completely.
In a large bowl, beat the remaining butter until creamy. Beat in half the confectioners' sugar until fluffy, then beat in the remainder. Add the marshmallow cream and beat until combined. If the mixture is too thick to pass through a squeeze-bottle nozzle, stir in a tablespoon or so of water.
Fill a squeeze bottle or pastry bag with about 2/3 cup of the marshmallow frosting. Insert the tip of the bottle into the top of each cupcake and squeeze frosting into the center. Spread frosting on the top, sides and bottom and sprinkle the cupcakes with toasted coconut.