I have a zebra hen who appears to be losing feathers. She's one of my most recent additions, I have had her for... a month, maybe? Got her together with another hen, from a person who was selling all their finches.
A week or two ago I noticed that she'd lost a few feathers on the back of her head. I kept an eye on her, but figuring maybe it was due to the stress of moving or some uneven/odd moulting. However, the patch seemed to grow a bit bigger. At this rate I started to worry that another bird/s were picking on her. I've tried to keep an eye on them, I can't watch them while at work, but from what I've seen while at home, I can't see any obvious signs of her being an outcast - she eats and sits with the others, isn't chased around the cage etc.
Of course, then the worry turned to disease, maybe something infectious... None of the other 6 birds in the cage show any signs of losing feathers thought (yet?). I admit I've avoided handling her as she's not tame in the least and if it was stress-related I didn't want to make it worse. But I took her out today to look for possible scratches or... lice, or something. Whatever birds can get that's visible to the naked eye. I couldn't see any sign of injury, although the area just seems to keep getting bigger and bigger

Here is a photo I got of her today:

I should perhaps mention the bright flash of the camera makes it look like the whole area is scabbed over - it doesn't look quite that bad in RL, there are no visible wounds or similar, just hairless patches along her neck, back and now out on one wing.
I've never had a sick(?) finch before, so I'm not sure what the best action is. What would you all suggest I do?
So far I've not isolated her from the others as I don't really have a good cage for it... but I can put her in the transport cage if you think I should. None of the other birds (including the one I got together with her) show any signs of suffering from the same thing, whatever it is.
Any tips welcome!