How do I get my dog to stop barking early in the morning?

The other thing to consider is what is motivating her to bark? Is the cause something you can change or control? If not I agree, ignore the behavior as anytime you give it audience you are reinforcing it. Possibly give her an alternative activity like a Kong, have it prepared the night before and just prior to when the barking typically begins, hand it to her. The distraction may get her beyond that early morning calling!

If she gets up everytime the dog barks, then she's already trained the dog. That is she trained the dog to bark so she gets up. Now you have to retrain. If a dog gets rewarded for any behavior, good or bad that's what the dog learns. You may have a few sleepless mornings before the dog gets it. Ignore her even if she goes on for hours. As soon as she's quiet then reward her. If shes alone somewhere when she barks you can hide close by and when she barks startle her with a loud noise and say "Quiet!". Do it until she gets it. I always say Quiet when my dogs bark after I get their attention. If you yell when dogs are barking they think you are joining the barking, and bark more. It's a pack thing.