Preheat the oven to 350 degrees F. Grease a large oven-proof baking dish. In a mixing bowl, whisk the eggs, sugar, nutmeg, vanilla, and rum together. Whisk in the milk and coconut milk. Add the butter, fresh coconut and bread crumbs. Whisk well. Pour the mixture into the prepared pan. Bake for 1 hour. Remove from the oven and cool for 10 minutes. Increase the temperature to 450 degrees F. Spread the meringue over the top of the pudding evenly. Place bake in the oven for a couple of minutes or until golden brown.