Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9 inch Bundt pan.

In a large bowl, combine the flour, baking power, baking soda, sugar, eggs, cherries, pineapple and walnuts. Stir by hand with a sturdy spoon just until blended. Spoon into the prepared pan, and spread evenly.

Bake for 40 to 45 minutes in the preheated oven, or until the top springs back when lightly touched. Cool, then invert onto a serving plate. While the cake cools, mix together the butter, confectioners' sugar and vanilla in a medium bowl with an electric mixer until fluffy. Stir in the cream cheese, and beat until smooth. Frost cake with the icing when completely cool.