Yes, it's possible to move the litterbox and then after they'll use it. Though cats don't like changes especially the litterbox, it can be done.
Some cats can adapt to certain changes but best is to move it bit by bit like move one or two feet each day. and in between just nudge the litterbox...
Can you inform the vet that you may be late due to getting Dynah into the carrier so that you don’t miss the appointment.
Leave the carrier open in her room till Monday. Sprinkle some catnip inside the carrier. Also try getting her toys in it so that she can go in to retrieve it and not be so...