I'll stay away from the quarantine issue since that is not your question, other than to just mention it.
You can expect them to establish a pecking order. They do that by pecking and sometimes fighting. A successful integration is when they get through this phase without drawing blood. At those ages, I would expect your bantam to be the dominant chicken, just because she is more mature. Don't be surprised when they all grow up if she remains dominant. Dominance is more about the spirit of the chicken than about size. Whether she will hurt the other three or they will hurt her, I can't tell you. That depends on the personality of the chickens. If you have enough space, provide different feed and water sources so the dominant one does not keep the others from eating or drinking, and, if you can, house them side by side a few days before you actually let them at each other, I think your odds are pretty good. But I am not going to give you any guarantees.