Can a broody hen with eggs be moved?

[Nashonii]

As a person new to chickens, I set the nesting box for the hen I bought (and was told was broody) 4 ft. above the floor, so she would be with her mate and coop mate, to entice her to go broody sooner. I was thinking she might be too nervous in a new home to start brooding. Well, it worked! We have had them 3 weeks and she is setting on her egg! (Second day!) Yeepee!
Now the problem. Can I move she and her egg down to the floor (so the young one won't fall once he starts walking,) without bothering her broodiness? Please tell me how.
We have built a separate pen for breeding and broody hens, but haven't' finished it yet. It will have a fence around it to keep the dogs away until the chicks are less interesting.

 

[Happy Chooks]

In my experience, most hens will freak out when moved. This can also break their broodiness. A hen will not normally take the chicks off the nest for a couple of days. For that reason, I let them sit wherever they choose, then once the babies hatch, move the hen, babies and any unhatched eggs at night to a safer location.

The exception, of course, is if they are brooding in an unsafe area - like outside the coop where predators can get them.