Dragoon generally benefit from carpenter for weapons, armorsmith for armor, and goldsmith for accessories. Leatherworker is also recommended to supplement and support the mats you need for armorsmith and carpenter. You also benefit from mining and botany to gather materials for those weapons.

That said, if you are crafting, you will want to level all crafting classes. This is because their cross-class skills greatly complement each other and ensure more reliable HQ. This gives you better items, at a cheaper cost, and without needing to rely on RNG. Most players level crafters all at once, although I would recommend you start out by leveling all crafters to 15, for the first set of cross-class skills. Having access to those first set will greatly improve your success rate and guarantee at least an 80% chance to HQ an item.

I would suggest you at least finish the lv.41 quest: In Pursuit of the Past first, before pursuing a crafter/gatherer class. This will let you access the Ixali Beast Tribe quests, which can greatly speed up your leveling for crafters and reduce your gil costs for leveling a crafter.