A single bird is a tough integration. She has no friends, and all see her as the stranger. The above poster, added a flock, which means the pecking was spread out over more birds.
I would start with the separation, but not for too long. I would add one bird to her but not in the dog crate...way too small. I would turn out the original flock into the yard, put the new bird in your run with a middle bird, and leave them there for the day. This will allow her to adapt to the new surroundings without being attacked by the whole flock, find the hide outs, the water and feed. If you can hold food from them so they are hungry, and feed along the run fence line. This makes them eat close together but safely.
If you are worried about eggs, put a temporary nest near where the birds would go back into the coop or run. Do not let the birds into the set up, till it is nearly dark. The original flock should go almost straight to roost. Might be a few fights, but unless blood, let it go.
The next morning, all might be fine. If so it would be good to let them out the same way as the day before, and then it should be a go. If there is one or two of the original that are very mean, lock them up, letting the new one work with a smaller more friendly group.
It is a lot of messing around to add one bird. Adding a pair is better, adding a bunch is best. But eventually it will go as long as you have enough room to add chickens, some obstacles and hide outs in the run, and a couple of feed stations and waterers.
M
