Darkmoon Defender

As far as i've tested, you have to Remove Insignia and loot corpses to get those Darkmoon Artifacts. Just got one doing it!

EDIT: Just got all 3 Artifacts. They definitely are looted when you remove other players insignias. Just keep doing it and they will show up.
EDIT 2: And of course, as said above, you have to get Darkmoon Adventurer's Guide from Selina Dourman and keep it on your bags.

Collecting all the Darkmoon Faire Artifacts listed below will give you this achievement. The full list of Darkmoon Faire Artifacts and the quest related to it are:

1. 
   
2. Fallen Adventurer's Journal & The Captured Journal
3. 
   
4. Banner of the Fallen & A Captured Banner
5. 
   
6. Captured Insignia & The Enemy's Insignia
7. 
   

To begin gathering the artifacts, Blizzard has stated (Source):

In addition, the [item=71634] can be obtained from [npc=10445], who resides in the first tent on your left as you enter the Darkmoon Faire ground on Darkmoon Island.

The Darkmoon Faire Field Guide

It’s your passport to riches, my friend. Y’see, we need a few things -- just some junk, nothing valuable to a big hero like you. We call ‘em Darkmoon Artifacts, and there’s all different kinds to be found all over Azeroth. The Darkmoon Field Guide helps you discover artifacts while you’re explorin’ dungeons, slayin’ monsters, and fightin’ in Battlegrounds. Without a guide, you’d never notice ‘em, and it’ll help keep you focused on the stuff we want. Whether you just reached level 10, or you’ve crushed the biggest baddies in the land, we need somethin’ from nearly everybody. You won’t have to go too far out of your way to get ‘em and each month you’ll get a new opportunity to seek out an Artifact for us. What do you get out of the deal? Don’t you worry, you’ll get your cut. When you bring a Darkmoon Artifact back to us, you’ll get valuable experience (it builds character, you know!), earn a better reputation, and possibly earn precious Darkmoon Faire Prize Tickets too!

I just achieved this. Simply looted all corpses I could. Found two in Warsong Gulch, and furthermore proceeded to loot all 3 in an Alterac Valley right after :)

If you don't turn in the quest, You are still capable of looting an identical questitem. However, it is completely useless, unless you want to give them to a friend. This is because you can't do the quest again.

Since they aren't BoP, I SUPPOSE you could trade them to a friend - Needs testing tho. Can be traded to a friend!
Also note; These can still be looted AFTER delivering them :)

Goodluck! Shouldn't take too long :P