After they burned down the beach house, she and Zuko went back to their old beach house. In one of the old cabinets, they found a bottle of rice wine and shared it, pretending for a little while that everything was normal, and they really did get along. They fell asleep in that dusty old house holding onto each other. She will ignore her hangover into submission. If she rises with the sun and does her katas just like any other morning, it will give up and go away.
The princess of the Fire Nation is never less than perfect. Hangovers are not perfection.