I never separate mine, I put them in at dark, and the next morning, I let the broody decide what to do. I think it is important for them to be in the flock.
If you do separate them, only do it for a few days.
Get her a couple of live day old chicks. See above advice how to give them to her.
The thing about giving her eggs now, is she could very well sit another 21 days and still not get chicks and still be broody. Or she might naturally break half way through. Live chicks would be best.
Mrs K
I would try this, grab a handful of those chick 3-4, at dark, sprinkle them with a little water, let them get a little chilled. They should be peeping madly, a little ways away from the coop, close enough she can hear them keep them just barely,. Wait 5 minutes. Then in complete dark, stick...