As much as I want to let the people decide, I really want to have our dragon daughter something to fall back upon when not running the empire as regent. She can show by example how the empire will be run under her by starting with the dukedom. As time goes on, people will witness and get used to how she runs things, therefore making it all the more easier to slip in as regent when no heir is available. Because dragons live for such a looong time, there's no doubt that opposition will fade with the passing of time, making it become the actual norm.
[X] Gift the Title: Well...your children could use some experience in the art of rulership. Gawain may be the first in line for the throne and already busy with his diplomatic posting besides, bbut you're sure one of your daughters would be able to make the most of the situation and put their skills and unique knowledge to use. Who knows, they might even learn something from the experience. Of course, there's the obvious question of who to give it to...