For the cake, preheat oven to 180°C. Grease 3 x 20cm diameter spring-form cake tins and line the bases with baking paper. If you only have one or two tins, work in batches, re-greasing and lining the tin between baking each cake.
Place the flour, macadamias, baking powder and oats into the bowl of a food processor and process until the mixture resembles a coarse flour. Do not over-process or the macadamias may stick together. Place into a large bowl and add the sugars, coconut, carrot and spices. In a separate bowl, stir together the yoghurt, macadamia oil and eggs. Add to the dry ingredients and stir thoroughly.
To make sure each layer of cake is approximately the same size, weigh the mixture in the bowl and divide the weight by three. Place one third of the mixture into each tin and bake for 15 minutes, until a skewer inserted in the middle comes out clean. Cool in the tin for 5 minutes before turning onto a wire rack to cool completely.
For the icing, place all the ingredients in a bowl and beat with electric beaters until smooth. Refrigerate to harden slightly. To assemble the cake, place one layer of the cake on a plate and spread with icing about ¾ cm thick. Add the second layer and repeat. When the layers are complete, top with the remaining icing, smoothing the top and sides with a knife. Decorate with dried fruits and fresh flowers if desired.