In order to get the plot of land in the Harthfire DLC in Dawnstar you need to do a quest but I can not seem to figure out what quest it is since I have a few dozen of them. What is the quest name and who do I have to talk to in order to get it if I don't already have it?

you have to do the Waking Nightmares daedra quest. Then if your lv 15 or higher the Jarl will ask you to go kill some giants. do that and he should sell you the plot of land. Just don't have ANY fetching type quests incomplete like finding someone a book or something. Those seem to interfere with jobs from the jarls.

So to get the Waking Nightmare Daedra quest I have to speak to the Jarl of Dawnstar?

nope. go to the tavern and talk with the priest. I think this quest is required to be completed before the jarl will talk to you about quests that lead you to becoming Thane and such. You don't need to be a thane to buy the property, only if you want a housecarl to patrol the grounds.

I believe it's lv 20, not 15, to get the kill the giant quest from the jarl.

Actually, it's level 22.