Any chance that you might've already done the quest "Eye of the Dragon" and simply forgot to equip the job crystal that the quest dropped into your armoury chest (bottom right icon)?
Does the journal show any quests related to dragoon, when using the dropdown menu to change it from "Disciple of War Quests" to "Disciples of War Job Quests"?
Have you tried going to the Observatorium (25,28 coords) in Coerthas Central Highlands, to see if there's a quest to pick up?