Preheat over to 350°.
To prepare bread, lightly spoon flours into dry measuring cups; level with a knife. Combine flours, oats, cinnamon, baking powder, baking soda, and salt.
Place brown sugar and butter in a large bowl; beat with a mixer at medium speed until well blended. Add water and egg; beat well. Beat in milk and vanilla. Gradually add flour mixture, stirring just until blended. Fold in carrot and raisins. Spoon batter into a 9 x 5-inch loaf pan coated with cooking spray. Bake at 350° for 1 hour or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack; remove from pan. Cool completely on wire rack.
To prepare frosting, place cream cheese and powdered sugar in a bowl; beat with a mixer at medium speed until fluffy. Beat in lemon juice. Spread frosting over top of cooled bread.