Preheat the oven to 350 degrees. Grease a 9x13 baking pan.
In a large bowl, sift together the flour, cinnamon, allspice, salt, baking powder and baking soda.
In a separate medium bowl, beat the brown sugar, granulated sugar, and the eggs together. Gradually add in the vegetable oil while whisking.
Slowly add the powder ingredients into the liquid ingredients.
Mix in the grated carrots and the crushed pineapple.
Add the batter to the baking pan and place in the preheated oven.
Bake for 25-35 minutes until a toothpick inserted into the middle comes out clean.
While the cake is cooling add the icing ingredients to a medium bowl.
Beat the icing until it is smooth.
Slowly remove the cake from the pan.
Spoon the icing onto the top and slowly spread it over the top for an even layer.
Sprinkle chopped raisins and chopped walnuts on top of the icing. Serve.