Can you move a duck egg from one spot to another while still on the incubation process without the mother duck abandoning it?

No because the egg needs incubation at all times.

I suppose you could is move the mother duck with it, put her on a cushion or something.

It is illegal to move a wild duck egg [Migratory Bird Treaty Act (16U.S.C. 703-712)] . You can be cited if an officer sees you. Even lifting the eggs destroys them and the ducks will continue to nest with no possibility of them hatching.

Not to mention you may be beaten senseless by the couple who's eggs you're trying to move. They get really mad if you get within 5 feet of a nest.