My dog got up this morning and her tail, usauly wagging is drooping.?

try playing with her. if her tail will not wag no matter what you do taking her to a vet is a good idea

I have Shiba Inus and their tail curls up but when they are tired, nervous, or sad it unwinds and hangs limp.That's weird about the whining and waking up in the middle of the night but maybe she heard something that you couldn't that made her nervous. I would just go about a normal routine and see how she is and if anything seems out of place for a day or two consider a visit to the vet.

She may need her glands squeezed. I know when one of my Lhasa Apso's needed that done, and his glands were impacted, he stopped holding his tail up.

I'd just suggest that you go to the vet next week, if it doesn't seem like an emergency.

there is a condition in certain breeds of dogs called cold tail

http://www.woodhavenlabs.com/coldtail.html