I would say a rewards chart for dry nappy or even to begin with a chart for taking her pull up off as soon as she gets up then progress to a chart for a dry nappy.

She may not be ready to be dry overnight yet but she certainly knows that she can go to the toilet when she is awake so I would think that taking her pull up off as soon as she gets up and not putting it on until right before she goes to bed would be the first step and then do the dry nights thing.

Just a thought - what if you put undies on under the pull up?