Some chicks are like this. My personal thought, (nothing real sciency, get another opinion) is that is is just a large amount of yolk that the chick absorbs just before it hatches.
It sounds like she has cold feet. My birds do this to a lesser extent in the winter. It could be molting as well. If there are no parasites, it could be picking.
Sounds like a sinus infection for most of them, but I could be wrong. I handle a lot of poultry for my job, but I only am in contact with them for a little while. My own poultry rarely get sick.
I use the PVC poultry tractor. I have 2 10x10x2 foot tractors for both chickens and turkeys as they are ready. I am using an 8x10x2 for a brooder. I found that coons can rip through poultry fence, so I am using 1/2x1/2 welded hardware cloth.
Actually, this is probably really good. They will eat the feed that the rabbits spill, and 'fluff up' the rabbit poo, helping it compost. I know many people who keep their rabbits above their chickens for the winter, and it is a great arrangement all around.
I would keep her alone. How long are you going to be watching them? Make sure that she has plenty of food and water, and keep her warm. Is there any way you could post a picture? Knowing their age and/or size would help......