Preheat oven to 180°C. Coat two 23 cm round cake pans with non-stick cooking spray.
Stir together flour, cinnamon, baking powder, bicarbonate of soda and salt in a medium bowl.
Beat sugar, oil, eggs and apple sauce in a large bowl until thoroughly combined. Beat in flour mixture just until evenly moistened. Stir in the carrot, pineapple and juice, raisins and walnuts. Divide batter between prepared pans.
Bake until a skewer inserted in the centre of each cake comes out clean, 45 to 50 minutes. Transfer the pans to a wire rack. Leave to cool for 30 minutes. Turn cakes out onto racks. Leave to cool completely.
For the icing, beat cream cheese in a large bowl on low speed for 1 minute. Add icing sugar and vanilla essence; beat just until smooth.
Place a cake layer on a serving plate. Spread with a third of the icing. Place second layer on top. Spread remaining icing over the top and side of cake.