Yes, exactly that, A short series of quests, actually.
And then, unless Blizzard changed things in the pre-patch, you need to gather a series of “Dragonriding Glyphs” to power it up. When you first get Dragonriding/Skyriding without the Glyphs, it’s a very poor experience, so you want to apply the Glyphs ASAP. Once you have all the Glyphs, you can fly at 910% speed (728% in other expansions) as much and as far as you want.
Take a character to Chromie. That Night Elf Hunter you are posting on will do fine.
Chromie is under the tree in front of the door of the Stormwind Embassy, near Stormwind Lake. You will find the Embassy marked on yoir map.
Tell her you wantto go to the Dragon Isles / Dragonflight expansion. She will give you a quest to sail there from the Docks, after rounding up some characters.
You will arrive at the Waking Shores, where you do maybe a dozen quick intro quests around the starting area, and are then sent south.
Keep following the quests, and they will lead youto the Ruby Lifeshrine, and the quest Dragonriding.
You then do a couple of simple glides, and you get your first Dragon.
Great! But Skyriding/Dragonriding is pretty lame at first. You get only three charges of Vigor, and it runs out fast. You want the Glyphs
Two or three hours should cover the whole thing, I think.