She was still on the roost to avoid the others. She is obviously intimidated by them, but her being in new surroundings may contribute to her timidness. Most chickens really hate any change. They are such creatures of habit.
They are going to have to establish the pecking order. As long as she is not hurt, I would not take her out. I don't know your set-up, but some things I would consider doing.
I'd set up at least two eating and drinking stations. The dominant ones will keep her away from the food and water as part of the intimidation process. If you have room, set something up to allow her to eat and drink. Separate dining facilities will also reduce the potential for conflict if she tries to eat from "their" feeder. This does not always work the way you would hope it would. When I try to feed a broody with chicks in a separate area away from the other adult birds, the other adults think that is a special treat and they'll go wipe that food out before they touch their regular feeder although it is exactly the same type of feed in both. I can't tell you how to do this. You'll just have to look at your existing space and try.
I'm guessing your mini-coop is your quarantine pen, well away from the others. You might watch and see if one of your existing three is a ringleader in the attack. Take her out for a two or three days to see if that helps. Or take two out to keep each other company and just leave one with the new one. Then when you put them back together they are all confused and the new one is on more familiar territory.
You can try to distract them by giving them some treats to work on. This won't keep them busy very long, but it gets their mind off being terrorists and onto eating. It seems to help get them to accept the new one a bit. After they finish the treats they may go back on the attack, but sometimes the renewed attacks are not as vicious.
If you can house the new one for a few days with the others but behind wire where they can see each other but not get at each other, it seems to help reduce tension a lot when you do put them together. Not everyone has a set-up where they can do that.
Sometimes nothing helps except to let them go at it. One of your existing hens may just be a mean sadistic bully. Your new hen may be such a weak-spirited chicken that the others will always pick on her. So much depends on the individual personalities. Most integrations like this are eventually successful but sometimes they are not very pretty. I wish you luck!
