Cream the butter and sugar together in a mixing bowl. Beat the eggs into the creamed mixture one at a time, and then beat in the vanilla. Combine the flour, baking powder, salt, and baking soda and beat these dry ingredients into the creamed mixture. Fold in the craisins, oats, and orange peel, then stir in the white chips. Place rounded tablespoonfuls 2 inches apart on baking sheet covered with parchment paper, and bake in an oven preheated to 375 degrees F until the cookies are lightly browned (10-12 minutes). Cool and serve.