No you don’t need to. All you need is a tier 3 garrison, which just costs a lot of garrison resources and gold. Once you upgrade that you’ll get the Tanaan intro quests and the shipyard. No other quests are needed.
That is from Baros Alexston, the head guy in your Town Hall. He’ll already have the upgrade quests which you use with the building table next to him. Tier 2 requires 200 resources to upgrade, tier 3 is 2000 and an extra 5000 gold.
There’s a pile of crates next to your Town Hall that builds up resources over a few days, but there’s a faster way than waiting on that.
Fly to Tanaan and go to the far east coast past the Dark Portal, there’s several rares there that drop a lot of resources once per day. Marked as stars on your mini map. And there’s another three in Highmaul in Nagrand, the open outdoor area, not inside the raid. Kill those six every day and it’ll take maybe 2-3 days to get the 2000.
All daily things, rare kills included, reset at a set time. I think it’s 8am PST? Or 3am? Honestly I have no idea which. Years of playing WoW and I still lack some basic knowledge.
But tomorrow generally they’ll reset. It doesn’t matter when you killed them. If you loot them a minute before the reset then you can do it again right after.