Yes of course! In fact, I have made this exact recipe using vegan substitutes in the past. Simply use a vegan non-dairy butter alternative in place of the butter and replace the egg with ¼ cup vegetable or other flavourless oil. The oil will help to bind the ingredients. The vegan version of these cookies may produce a slightly runnier batter dependent on the type of non-dairy butter used, but otherwise they will bake quite similarly. Another alternative for the egg, is to use peanut butter instead of oil. This will produce an oatmeal peanut butter cookie, and the taste of the peanut butter will come through in the finished product. This might work for you dependent on your preferences, but I'd not necessarily recommend if you're not aiming for something peanut-y!