It is not a good use of your counter service credits to get a breakfast.
One option is to pack some breakfast items in a small suitcase. I personally like Lara Bars, oranges, peanut butter, whole wheat crackers, dried apricots and the like. My kids know that they only get pop tarts when we are on vacation, so a few of those might be a nice vacation option for any kids along. Grab your breakfast items and your refillable mug and head down to the food court and get some tea or hot chocolate and enjoy your drink and breakfast items.
When the bag is empty at the end of your stay it becomes the extra space you need to bring back all the little extras

you had to have while visiting the great and mighty Mickey.
Another option is to use your snack credit in the morning to purchase a smoothie, large muffin, bagel, fruit, or junk food

and pair that with your refillable mug. That should get you moving for the day and fuel you until lunch time.
Another option is to ask for whole fruit, or a muffin, or junk food as dessert from your counter service meal and then save it for breakfast the next morning along with that refillable mug.
I find counter service offerings and the ease of mug use great in some hotels and miserable in others. If you are at the Contemporary or Wilderness lodge you just zip down the elevator and there you are!
If you are at the Poly or Boardwalk Inn it can be a much more convoluted journey to get your mug filled.
Breakfasts are the least expensive meal. So pick up an oatmeal

for a couple of dollars and a piece of whole fruit

for a dollar and have a wholesome, hot, and nutrient filled breakfast for a few dollars.