It means you don't have your Dragoon job crystal equipped, which turns you from LNC to DRG, allowing you to pick up the quest. Open your Armoury Chest, and click on the icon shown in the following screenshot:

If the job crystal isn't in there, it might be in your inventory, or on a retainer. Try typing "/isearch dragoon" (without the quotation marks). If it comes up with the item link "Soul of the Dragoon", right click it and click "Search for Item". This'll show if it's in your inventory, or which retainer it's on. (As an added note, the /isearch <item name> command is really useful if you can't find an item on your character.)