The hat in this outfit is a light armour piece, but I would urge all burglars going through Dunland to pick it up! I have found it in one place only as a reward from Théodred’s Riders, so it’s not a very common reward. Especially hobbit burglars should not miss out on this one, it’s just too cute to skip!
If you want to know where a certain armour piece or cosmetic comes from, you can look it up in the Lorebook, by typing its name into the search box.
Head: Elegant Silk Hat, black dye (Isengard quest reward, light)
Chest : Chestpiece of the Charging Stag, black dye (Dunland quest reward, heavy)
Shoulders: Westfold Skirmish Pauldrons, black blue dye (crafted, medium)
Hands: Heavy Plated Dunlending Gauntlets, black dye (Dunland quest reward, heavy)
Feet: Threadbare Shoes of the Dunland Healer, black dye (Dunland quest reward, light)
Cosmetic Lotro 
You get at least two chances to catch one of these hats in early Dunland quests. I think one in Trum Dreng and the other in the Bonevales.
Good to know! I know that in the early areas I had to make some tough choices regarding rewards, and it might be that I skipped it in either of those two areas, but I don’t remember seeing this particular one. There are a number of light armour hats though that are quite similar, and even have an exact same icon, which is confusing.
I just took a picture of my minstrel wearing one of the early available versions of that hat. Honestly I can’t make out any difference. Have a look: http://img338.imageshack.us/img338/8670/huty.jpg
Unfortunately I don’t seem to have a decent computer at my disposal, so the quality of the picture is far away from your standard. Sorry for that, but to me the hat seems identical.
It’s the same hat! Good to know it is available at least twice.
The version of that hat I got is called “Threadbare Hat of the Dunland Healer”. I got it from a level 67-ish quest. Very cute!