It is terrific that she's able to wake when she feels the urge – some kids don't get that part till years after daytime training. But her bladder is still very small, and her kidneys just keep on doing what they're supposed to. Try to stay patient, her bladder will eventually increase its capacity, and her sphincter will gradually be able to hold out until morning.
I have two suggestions. You might consider putting a small potty chair in her room to keep the waking time to a minimum. Experiencing less arousal during the event might possibly help her learn to sleep through more easily, but that's more a guess than good science.
Also, sleep happens in cycles, and at the end of each 1.5 to 2 hour cycle, the sleep is fairly shallow and the child easier to wake briefly. Assuming your daughter goes to sleep around 8 p.m., she's probably waking after her second, or occasionally third, cycle when her sleep is shallow enough for the bladder signals to get through.
So you might look for a time around 2 hours or less after she falls asleep to see if you can rouse her and take her to the bathroom; if this coordinates with your own bedtime, that might be enough to get both of you through the rest of the night.