So far its only been confirmed for Free Companies, with private housing still unknown and to be honest is of little use, because you will be giving up your original plot, thus loosing your investment. The only way your going to get any Gil back is, sell your plot to another player or wait 45 days without entering your house to get 80% of the purchased price back.

This is setup for FCs to move and keep chambers, workshop and Airship voyage status, possibly not actually moving the airship/s them selves as they don't say it... you might have to remove them prior to moving, its not clear yet.