Grease two 9-inch cake pans and line with parchment circles. Preheat oven to 350 degrees F.
Grate the carrots using the grater attachment on a Food Processor , or use a Box Grater (if using the box grater, use the finer side) .
After they are grated, use the blade on the food processor to chop the carrots more finely.
In a small bowl whisk together the flour, baking powder, baking soda, salt and spices. Set aside.
In a large bowl, whisk together the sugar, brown sugar, oil, eggs, vanilla, and zest. Whisk in the dry ingredients, just until combined. Using a spoon, stir in the carrots and dried fruit.
Fold in the coconut.
Divide the batter into the two prepared pans and bake for about 30 minutes, or until a tester comes out clean.
Let cakes cool completely in the pans on a wire rack.
Make the icing by blending the cream cheese, butter, vanilla, lemon extract, lemon juice, confectioners' sugar and Lyle's Golden Syrup, until smooth.
Put one of the layers of cake on a 9-inch cardboard round and then top it with 1 cup of the cream cheese icing.
Cover the cake with a thin crumb coat. Then finish with a smooth coat of icing on the cake. I ran my spatula tip around the icing to create the swirls, but you'll be pressing coconut on the outside, so don't worry about getting this effect.
Before moving the cake to the platter, lift it and gently press the shredded coconut onto the top and sides.
This cake is wonderful the next day or even the following. Just wrap it well and refrigerate....if there is any left!