Is it possible to move a killdeer nest?

Before I tell you the answer, let me just say that there are laws prohibiting any disturbance of a migratory bird's nest and there are fines and penalties for doing so. That said, they should only be moved if absolutely necessary and only if the only other option is the destruction of the nest.

Yes, it is possible, but it has to be done very, very carefully or the bird may abandon the nest.