Heat oven to 350ºF (175ºC). Lightly coat the bottom of an 8-inch (20 cm) round cake pan with nonstick cooking spray. Line with wax paper and lightly coat paper with spray.
In a small bowl, combine flours, baking soda, cinnamon and salt. In a large bowl with an electric mixer, beat eggs, honey, oil and lemon juice until blended. Stir flour mixture and carrots into egg mixture just until well blended.
Spread batter into a prepared pan and bake until toothpick inserted in center comes out clean, 30 to 35 minutes. Cool in pan 10 minutes. Turn out of pan and cool completely.
Meanwhile, for frosting, beat together cream cheese, powdered sugar and vanilla in a small bowl. Spread a thin layer over cooled cake and serve.