Substitute for dry milk powder
You could replace it with any other powdered non-dairy milk trivially, but I imagine you don't have those either. There's also not enough liquid in the recipe to be able to reduce it and use actual milk.

That being said, the purpose of milk in baked goods is flavor, a tender crumb and a well-colored crust. You could add in a tablespoon of peanut butter or another fat (a local bakery makes dog biscuits with rendered bacon fat) to add tenderness to the biscuits, and your dog will probably appreciate the flavor while you can avoid the issues of canine lactose intolerance.