Preheat oven to 350ºF and grease a loaf pan; set aside.
In a bowl, combine flour, orange zest, baking powder, baking soda, ground cinnamon, and salt. Whisk until blended and set aside.
In the bowl of a stand mixer, add butter and sugar. Using the paddle attachment, process on medium-high speed until the mixture is creamy.
Add eggs, one at a time, and mix well between each addition.
Add half of the dry ingredients and half of the eggnog. Reduce speed to low and process until just combined before adding the remaining flour mixture and eggnog plus rum. Gently fold in cranberries and walnuts.
Pour the batter into the prepared loaf pan and evenly level it out using a spatula.
Transfer to the preheated oven and bake for 55 to 65 minutes or until a cake tester inserted in the center comes out with just a few crumbs.
Remove from the heat and let it sit in the pan for 15 minutes before unmolding and placing the bread on a wire rack to cool completely.