In a large bowl, combine nectar, coconut milk, and 1 teaspoon rum extract. Sprinkle pudding mix over liquid and whisk for 2 minutes. Fold in coconut and 1/2 of the whipped topping.
Pour into pre-baked pie crust and chill in refrigerator for at least 3 hours.
Combine remaining whipped topping with 1/2 teaspoon rum extract. Top chilled pie with whipped topping and toasted coconut.