How to get dragons as Daenerys?

Hi, has anyone figured out how to play as Daenerys other than waiting for decades for her to spawn with an event, if she even does appear (even with the game rule).

When you play as Daenerys from the start (when Rhaegar dies, Aenys gets the event to send the rest of the family away where they get land around Pentos), when does she get dragons/eggs?