There is an old wives tale that says having enough to refill depends on which side of the moon the digging happens. However, the answer is a little more scientific. A dog's digging scatters the dirt to smithereens (whatever that is) and it is impossible to gather the same amount the animal happily, care-freely, blissfully, mindlessly distributed hither and yon.
I would stop by a Walmart (or Home Depot, or Lowes, or...) garden shop and pick up a cheap bag of dirt (not expensive potting soil). Bags are a manageable amount to handle both at the store and at home even if I needed two or three.