@Plinky my first reply would be failure to thrive but if she appears to be normal sized as in ... not her overall weight but carrying average weight and meat on her bones that probably isn't the case. Or if she was normal before and now loosing weight. Second question is, are you sure first off she isn't a bantam brahma as opposed to a large fowl? A large fowl brahma will be about 7 months old before they lay so it can start at any time now. My guess is the weird eggs you got are simply pullet eggs from the other layers. That's not unusual at all even if they have been laying normal eggs. It happens quite often and when they get ready to molt later and finish a molt it will probably happen then as well. I have to disagree on the weight for a 6 month old brahma large fowl. Brahmas are huge birds and take a long time to get there. They will be a year and a half before they reach full weight.
Also considering she is a brahma and you mentioned one other bird was a leghorn brings up another concern. Brahmas are the gentlest of all bird breeds. They may grow huge but they are very easily bullied and may seek refuge alone to avoid being picked on. You don't mention the other breeds you got. If it is sex links, rocks, and some other birds particularly smaller built bodied birds then it is very likely she is just avoiding the others because she is a victim.
Her symptoms don't sound like Mereks at all. I'd forget that consideration. And mereks can infect chicks that
have been vaccinated. It just simply reduces the liklihood and usually if contracted makes the symptoms milder initially. She would have loss of control of one of her legs or her head or wings. It's equivelent to being paralized on one side. If she is walking normal and carrying her head normal that is out of the question Mereks unfortunately will drag a chicken down really really fast.
The loosing of feathers and picking is quite normal at this age. Pullets have a pre egg laying molt and that is normal behavior. The very first thing I would do is take her temperature. Not once, but several times in one day. Chickens temperatures fluctuate as they digest food,rest , and whatever other behaviors. Her temp regardless should fluctuate between 101 and 105. Yes you need to take it in the vent. In fact it's a good idea to buy a cheap little digital thermometer just for your first aid kit for chickens. You certainly don't want to get it confused with one you use in your own mouth!
If it is above 105 and stays high she has an infection of some kind and will need antibiotics. And I say digital because most chickens aren't going to want to sit with a thermometer in their vent very long.
You did mention one thing that is a very strong possibility. She could very well be blind. Being so, she would have trouble finding food and water. I had a blind turkey for years and she depended on chickens to know where food and water was. She also learned the sound of my voice and would instantly start pecking around her then cause she knew I was feeding or watering. It would be fairly simple to test that theory. I've had a few chicks born blind who fed well as chicks, I assume responding to the other chicks noises but failed later. Talk to her when you feed her. Help her find the feed and make sure she has access to water easily. The dry poop may be another consideration in the fact she could be blind.
If it were me I would separate her and give her a clearly controlled environment where her feed and water are always in the same place and that you always talk to her when she is getting fresh feed and water, making a point to guide her that way. It won't be long before it's apparent if that is the problem. Keep the space reasonably small but large enough so she doesn't feel trapped. I like using medium wire dog kennels for hospital rooms for things like that. I she able to get up on a roost and not fall?
Other questions. Have you watched her breathing? Does it seem like she breaths without gasping or sneezing or struggling in any way? Have you noticed anything at all other than that that seems different? Is she sneezing or coughing at all? What color is her poop and does ti vary from your other chickens'?
Now back to failure to thrive. It's really all too common particularly in hatchery stock. The lines are inbred so badly in some of that stock, that simple problems begin to creep up especially internally. Things like heart and liver problems and twisted intestines. But failure to thrive can occur regardless of the background. Just like birth defects can appear in all species. Failure to thrive isn't really a disease. It's a condition caused by some other internal problem. Often the cause is never known until the bird passes and if a necropsy is done sometimes the cause will then be apparent.
My advice is to rule out the obvious problems. Take the temperature. Separate her and make sure if she is in fact blind or not... and see that she learns to find the food and water without too much effort.
My blind turkey I mentioned by the way, just died this spring at 5 years old . She laid eggs and seemed to enjoy her life as long as she had her chicken companions to show her by sound where things were. She even adapted and roosted on a nest box that was installed on the floor. She always talked to me and headed out to the pen when she heard my voice cause she knew where to find her food and water. I didn't mind giving her a structured existence so she could function well. The one thing I couldn't do was let her in with the other turkeys because if someone tried to breed her it just scared her to death.
One more short thought on this. I had a chicken that was born hermaphrodite. This bird was always by itself and never crowed and never laid an egg. It never tried to breed a hen and no rooster ever tried to breed it. It did use to run to me when I was out feeding and jump in the wheelbarrow and eat like it was starved while I was going from pen to pen. It had saddle feathers like a rooster and a comb like a hen. At about 8 months old it started failing really fast and I couldn't find any thing wrong with it but it was loosing weight and then later started running a fever. When it died I did a necropsy. I found not only gonads a rooster has but it had a shelless egg stuck in it's vent and apparently died from not being able to lay the egg. It wasn't perintonitis that one would normally see, but obvious infection because the egg was blocking it's ability to poop and get toxins out of it's system. I always said it had to be hermaphrodite but the necropsy proved it beyond a doubt.
So there's a lot of possibilities out there.
Try a couple of these things and see if you can first make sure she's not running a fever and secondly find out if she is blind. I don't know where you are, but after trying these things if you aren't far I'd be willing to see if I can find anything that might be causing her problems. No guarantees of course because I obviously have no way to check her internally.