One other thing you can try is that if she is constantly getting up at 6:00am to go outside then set your alarm for 15 minutes before hand so that you're awake before she is and can get her out before she starts to whine.

I agree with ParNone though in that she is whining to tell you she has to go potty and is then rewarded with getting to go out to potty.
I would probably do the same as she suggested in taking it out and then right back into the kennel afterwards.

IMO it's very helpful with potty training to have a dog that alerts you to when it needs to go outside.