What should I do about DumpsterDiver?

[feralpigeon]

There is this oh so cute in my eyes little pigeon at one of the buildings I take care of. I started feeding her about a year ago when I noticed that she would take these prolonged dives in the dumpster looking for food and then show up at my vehicle @ lunch time looking very pathetic.
We took to each other and before I knew it, she would follow me into the facility after lunch as if she was there on official business to help me.
Over the last couple of months her "bad hair day" has turned into loss of feathers and her head is virtually bald. She is also losing the feathers on her back between the wings and it is quite an effort for her to fly to awnings between the first and second floors.
I have thought of catching her and bringing her home to help her, I think she may have mites and who knows what else, but she does have a mate and a few weeks ago I noticed when she bent over to peck at seeds, there was an egg stuck to her hi-nee. What should I do ? I don't want to make her unhappy by splitting her and her mate up, I don't know where her nest is so I have no way of knowing if she has babies that she is attending to. Can anybody help me with advice on this one?
Thanks,
fp