I am slightly confused with what heirlooms to get if I want to play a DPS based death knight. I'd like to equip first for full exp gain followed by whatever will help me produce the most DPS. I plan on getting as many heirloom (delta the ring as it's really a pain to win) before I start playing the DK.
Since you're a DPS you should get these:
The cape and the helm are available from the Guild vendor once your guild has reached a high enough level (10 for the cape, 20 for the helm)
Adding a Bloodied Arcanite Reaper to the mix may be a good idea: it may lack the experience bonus, but you get a good weapon that scales with your level.
All of the above would provide you a nice 35% bonus experience (until level 80, at which point spaulders and chestplate stop to work) and a good boost to your stats, scaling gracefully while you level.
If you still have Justice points in excess you can also get the Swift Hand of Justice: not a great improvement when compared to the other heirlooms, but a little haste and a self heal can help from time to time.
You'll need Champion's Seals to buy items from her, which are a reward from the dailies in the zone.
This area is not current content anymore, since it's been released in Wrath of the Lich King, and it takes days of work to unlock all of the dailies available.
It can be anyway a good source if you have nothing to do except waiting for the next Heroic to pop up. In the event you already unlocked the Tournament and you have many 80+ character it can even become quite profitable, since Heirlooms are bound to account and you can move them between your toons.