Small, dark and quiet is good for her right now. Could very well be reproductive issues or could be heat stress or a combination of both, but I would think after water and a day in the house, if it was the heat, she'd be perkier.
Chickaroo, a tsp or two over her food will be good. I just recently found that the extra virgin olive oil I gave some of my under the weather girls increased their circulation, or seemed to.
Lisa, I'm so sorry about your older hen.
I dont think it would hurt to give her vitamins and electrolytes in her water for a couple of days. You may try scrambling an egg for her, chop it into small pieces, and drizzle it with olive oil. If she's having crop problems, that might help her a bit. A great supplement is AviaCharge 2000, a...
Sure you can keep her in the dog carrier as long as she is cool enough in it. Taking her to a vet is entirely your call. Most regular vets know nothing about chickens, I understand. You could just try separating her and feeding her special food, etc., for a couple of days and see if she perks up.
The whining noise may be because she's in pain in her abdomen, so when you picked her up, she whined. It could be the heat stress is just the last straw and not the main thing that is wrong with her. Sexlinks are very high production birds and many of those get spontaneous ovarian cancers...