Have a new rescued chick, want to integrate it with my other chicks

FYI I posted this in the raising baby chicks forum as well but I am hoping to have more responses.

So I was given a very very sweet pullet that is about 5-7 weeks old yesterday. I want to integrate her in with my other 7 4.5 week old chicks. I just made an attempt to integrate and my one head cockerel chased her away and won't let her come close to the flock. My other pullets could care less about her, but my three cockerels, especially the head one, just wouldn't tolerate her eventhough she is bigger and older than he is. What should I do to help integrate them? While the sweet pullet was trying to get away from my head cockerel she got a tiny cut on her foot where the nail and skin meet. I picked her up and cleaned it off and stuck her in the brooder for now. She is just sitting in the brooder crying Should I put her in a wire mesh dog crate in with the other 4.5 week olds for a few days and see how it goes? I would bring her in at night of course. Oh I should also mention that this is the first night that the 4.5 weeks old will be in the coop, hence why my brooder in my house is free for my sweet pullet to use right now. What would you do? Thanks!

Per the suggestion of another bycer, I have removed the three cockerels and put them in my brooder and put my sweet pullet in with the rest of the 4.5 week pullets. The top pullet is the only one who seems to want to peck at the new sweet pullet. She goes for the eyes. It's not bad when she pecks, so I mostly just let it go and let them all figure it out for themselves. But how long should I wait to integrate my cockerels back in? Won't it just mess up the pecking order all over again?

Sorry for the long post, I am just trying to do the right thing.