I've done it, but have had mixed results. They can be very attached to the nest they've chosen and often will stop brooding, or at least spend all their time trying to get back to their spot and not sit on the eggs in the new spot.
I've had better (but not 100%) luck if I get the new nest set up in advance (a large dog crate works great!) and then after dark I pull the hen off the nest, stick her head under a wing to keep her calm and hand her to my daughter to hold. I then carefully move the eggs (I candle and discard and obvious duds while I'm doing this) to the new nest, put the hen on the eggs and shut the door to the crate. I put an old blanket over the crate and leave it like that until the next night. The crate is large enough for me to put feed/water in with the hen and for her to get off the nest to eliminate though that does need to be cleaned off daily. I have the crate in a covered 4x4 dog kennel and after the first 24 hours I open the door to the crate and take the blanket off too so the hen can stretch her legs a bit, take a dust bath etc.
I have found that if I don't cover the crate for the first 24 hours and keep the hen confined to the pen for at least a week that she will almost always go back to "her" nest. I've had about a 75% sucess rate doing the way I've described above. It's not perfect, but with all the preds. in my area a hen sitting on an exposed nest has almost no chance of staying alive long enough to hatch chicks.
I have occasional losses free ranging during the day, but the dogs are able to chase most of the critters off. The dogs stay in most nights so it would be open season on a setting hen.
