How big of a dog crate? Physical measurements? You need room for a nest, food, water, and a small bit more. A broody hen should know by instinct to not poop in her nest but the food and water are fair game. That means you'll need access to clean the food and water.Just happened to see this post. My hen started sitting a nest yesterday. Should I set up a dog crate in the coop and move her before she gets too far into this?
I'd wait until the hen has spent two consecutive nights on the nest instead of sleeping in her regular spot to confirm she is serious about being broody. I've had hens show all kinds of signs of being broody but not stay on the nest long enough to hatch eggs a few times. If she is not a committed broody she could easily break from being broody if you move her too early. She might anyway.
I'd move her after dark with as little commotion as possible and lock her in the new pen. I'd leave her locked in there until the chicks hatch. Sometimes the hen wants to return to the old nest. I wouldn't give her that option.
I moved a couple of hens but now I let them hatch with the flock. There are risks no matter what you do, move her or leave her. Broody hens have been hatching with the flock for thousands of years, they have not gone extinct yet. If you decide to not move her let me know and I'll talk you through that.
Good luck!