Know that there is a good chance of breaking her broodie if you move her. As Deb said, do it at night and somewhere you can lock her in for a few days so she won't try to go back to the place she chose. I moved my broodie over a foot because a rotten egg exploded and made a mess. I mixed clean shaving in with her original nest that wasn't too soiled and moved the eggs. What was pipped and peeping loudly. I came back a few hours later and she was back where she started and only took a few eggs with her...the pipping one was not one of the chosen and it got cold and died. Picky little things! Remember, people move broodie's to break their broodiness.
#2 I was surprised to hear she'd plucked her belly clean already. Mine plucked herself right before "lockdown", I felt to increase humidity.
I had not considered a "lockdown" for a broody hen. When would you do this?