You might have to restrict her to the cage and rather small surrounding for a few days if you want her to use the nest there. They have quite strong opinions about the right place. If she kindles somewhere else it is possible to move the nest, but I consider that to be more of an emergency option because it can cause problems, and you would have to confine the doe for some days too, better to do it before she kindles and let her accept the nestbox.
I would put the nest and fur in the nestbox, show it to her, and confine her to the cage.
It reads like you were surprised that she built a nest, you knew she was with a buck and is possibly pregnant, that it'S not a false pregnancy, right?
