On my character, Masashi, my shipyard is not there for my level 3 garrison. I know I already should have a shipyard because the quest “Let’s Get to Work” is shown as available as a yellow exclamation point on my map. This quest is part of the shipyard questline, and it becomes available only after you create the shipyard. However, when I go to the exclamation point on the map to accept the quest, there is no NPC nor shipyard for me to accept the quest from. I believe this might be a phasing issue? Hopefully you all will know better than me though.
I am going from memory here, but as I recall, soon - if not immediately - after you get a level 3 garrison, you should get a quest automatically to speak to Vol’jin in your garrison HQ. Following this quest a new quest sends you to the non-dungeon version of Iron Docks via the garrison flight master.
There follows a series of quests at the Irons Docks that net you both a shipwright and the plans needed to properly start your dock construction. You return to your garrison, start your dock construction, build your first ship, then proceed to do the Tanaan Jungle (endgame version) intro, set up your base, do some busywork quests like picking up flight paths, getting you “first” oil, then get sent back to your garrison to speak with the NPC at your docks and do the tutorial for the dock mission table. (Tanaan Jungle was where players originally got the bulk of oil for the shipyard, garrison missions came a bit later. The off-shore oil rig accessible via the dock mission table was a much later addition.)
If you have missed some part of the unnecessarily elaborate quest chain - even on a current level 80 it can take the better part of 90 minutes to do all the steps - you may need to go back to Iron Docks and Tanaan Jungle alt-tabbing between Wowhead and the game to find what detail you missed. Like not picking up the breadcrumb quest to return to you garrison at the Tanaan Jungle HQ, only to be sent immediately back to Tanaan Jungle HQ to purchase a ship plan.
It should also be noted that the Horde garrison dock area was always a bit flaky. More so now after the 20th anniversary added the “detective” story line for the Incognitro motorcycle mount. Which necessitated Blizzard to “do things” to the area containing the docks to make a clue accessible. Since the 20th anniversary event, I have had to fly around a bit and approach from the east side over the water to not trigger whatever they changed to make the clue accessible.
You are awesome. I went to the iron docks and the quest “Derailment” (part of the questline, but before the “Let’s Get To Work” quest) was available for me to start. So it was just the fact that my map showed the “Let’s Get To Work” quest when it shouldn’t have that was throwing me off. Thanks so much for taking the time to help out. I can grind the Captain badge now 
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Glad to have been of help. We’re all in this together!