She is currently in the flocks coop and it’s too high off the ground for her chicks to get out.
There are two parts to this. I've seen a hen get her chicks down from a 10 feet high hayloft. She said jump and they did, then ran to her. My nests are 2 feet and 4 feet above the coop floor. My broodies hatch chicks in them all of the time. They have no problems getting the chicks to the coop floor. The chicks cannot get back to the nest so she settles down on the coop floor and the chicks go under her to sleep or warm up. They have no trouble getting down from the nest and don't need to go back to the old nest so that part is not a problem for me or them.
One time I had a hen go broody in a nest in a cat litter bucket. That top was so small she was sitting right next to the edge. When a baby chick climbed on top of her and then fell off, it missed the nest on the way down and fell 4 feet to the coop floor. Four different times I had to pick chick up and put it back in her nest. Probably the same chick each time. Four times it fell and was not hurt. Needless to say I retired that nest after that hatch was over.
So what does your nest look like? Is the hen so close to the edge that a chick falling from her back might miss the nest and keep going? I don't know how big your hen is or how big that nest is. I can't judge whether this should be a concern of yours or not.
You are dealing with living animals, I cannot give any guarantees. Anything can happen. But growing up on a farm with hens hatching and having three or four broodies hatching each year in my flock this is the only time it has been a problem.
My question is could I move this hen to this new coop now before her chicks hatch out?
You can try, it often works. As Sourland said, the big risk is that she breaks from being broody. If you try I'd move her at night in the dark and lock her in her new coop/nest. Do not give her the option to return to her old nest. Many broody hens will accept that move but you don't get guarantees.
I don't know what your nest, coop, or flock look like. My broody hens hatch in the coop with the flock. It's not a big deal, but I have a lot of room and a flock that spends all day every day outside. If your coop is one of those tiny elevated coops I'd have concerns. I do not know what the right decision is for you.
