I agree, it would be best to separate her so you can keep a close eye on her. Hopefully, she doesn't have something contageous. Can she stand and walk?
Personally, I would try to get her to eat hard boiled egg yolk to get her strength up. I'm sure the white is fine for her too... good protein... I just feel like the yolk is more nutritious and it is every chick's "first food". Poly-vi-sol without iron is a great suggestion and a good thing to have on hand for emergencies.
She would be happier if you put a buddy in with her when you separate her, but if she has a disease you risk infecting the other chick too. It will be extra important to make sure that she doesn't get chilled, so hopefully you can keep it 95 degrees on the floor of her pen with a cooler place to go if she gets too warm. I love the snuggly hat-cave idea!
Poor girl! I hope she gets better soon!