The interesting thing about walking relative to jogging is that you burn roughly the same amount of calories per mile. It just takes you much longer to cover the same distance.
A moderate walk with the dog that doesn't get your heart rate up probably won't improve your cardiovascular health all that much (esp. if you're used to it), but it does burn calories, and thus is a Good Thing.
If you followed the dog's footsteps, you'd probably burn about twice the calories. After all, it's rarely a straight line between pee stops.