The biggest problem will be keeping it upright and stable and protected from wind during transport. A large moving carton would be very useful in that regard.
That said, if you cannot get it out the door, you may have to prune back some of the largest stems. But that should not be an issue as Dieffenbachias are fast growers and respond very well to pruning.
Good luck with the move and try to duplicate the light in the new location as much as possible.
