Pre-heat oven to 180C (160C fan-forced). Lightly grease a bundt pan.
Place oil, eggs, yoghurt, sugar and orange rind in a large mixing bowl. Using electric beaters, mix until well combined. Fold in flour, coconut and spice.
Add carrot to mixture, mixing well. Spoon batter into prepared pan and bake for 50 minutes. Allow to cool for 10 minutes in the pan before removing to a cooling rack to cool completely.
For icing, whisk together all ingredients until smooth. Drizzle over cake and decorate with edible flowers.