If you're the Horde, you'll want to grab an Utgarde Keep group to get your best possible bracers. The Vambraces of the Vengeance Bringer are gained from the Horde-only quest A Score To Settle, and are tailor made for a plate DPSer. Both sides can also get the Shaleground Bracers by clearing out the Vykrul settlement of Skorn via Westguard Keep or Camp Winterhoof.
Once again, you'll find the better non-dungeon option in Borean Tundra. The Freed Shackles are from the Tuskarr quest Leading the Ancestors Home, and provide a very nice chunk of strength and some hit rating.
Early quest glove upgrades in Northrend for a Death Knight DPSer seem to be sparser than other slots for some reason, but there's still a few options. In Borean Tundra, you'll be able to get the Bogstrok Plate Gloves by helping a guy in a Murloc suit, which provide a good chunk of strength and some expertise. Less desirable but still a solid upgrade over Outland gear are the Onyx Grips from Howling Fjord, obtained by Stopping the Ascension of the Thane at Skorn.
If you're tanking on your Death Knight, you'll once again want to consider some dungeon diving in The Nexus. The quest Postponing the Inevitable will get you the Gauntlets of the Disturbed Giant, a clear upgrade over the cobalt gauntlets, making up what they lack in strength with hit rating -- and as everyone knows, you can't gain threat if you can't hit your target.
Belts are actually about as sparse as gloves, and for once, the Howling Fjord option might slightly edge out the Borean Tundra option. The Gold-Plated Coldsteel Girdle offers a sizable amount of critical strike rating, with some strength and hit rating to sweeten the deal, making it a solid DPS choice. You get it by getting the quest to slay Necrolord Mehzen at Westguard Keep or Camp Winterhoof.
In Borean Tundra, consider grabbing the Girdle of Ripped Space from Monitoring the Rift: Winterfin Cavern. It doesn't have any hit rating, and it has less strength and critical strike rating that the coldsteel girdle, but it does have 58 Stamina, at the least making it decent for tanking if you decided not to spring for some Cobalt.
For leggings, Howling Fjord once again probably wins out for pure DPS. You'll actually get the Antique Reinforced Legguards rather soon after you get off the boat or zeppelin, either from the Anguish of Nifflevar for Alliance or The New Plague for Horde. They have the most strength of the plate leg quest rewards.
Howling Fjord completes its dominance of lower body DPS options with the Master Artilleryman's Boots, which provide a very sizable amount of critical strike rating and strength, and are probably the best of the normal quest rewards for DK DPS. Horde get them from Brains! Brains! Brains!, while the Alliance gets them from Preying on the Weak.
You do still have a few options in Borean Tundra. The Chilled Greaves have a small amount of strength and critical strike rating, but no stamina and some haste rating. Still, they're a solid choice for DPS. The Moral Sabatons gained from helping the DHETA are good in their own right as well, but they have raw attack power, which means you won't get the usual parry benefits from them. Still, 76 attack power is nothing to sneeze at, and it comes with stamina and critical strike rating as well.
Once again, Tanks are going to want to get a Nexus group. The quest Quickening gives the reward of the Boots of the Unbowed Protector, which provide a bunch of defense, dodge rating, and stamina, a clear upgrade over Cobalt Boots for tanking.
Gearing up and Rolling out
As you might have guessed by now, Borean Tundra is probably a slightly better choice for a Death Knight to begin their Northrend career in terms of quest gear, but Howling Fjord has some strong choices, and you probably won't go wrong leveling through either zone. Myself, I'm still leveling in Howling Fjord for now because I enjoy the lore, the scenery, and the music more than Borean Tundra, but even even I'm nipping over there to grab that axe.
Either way you choose, welcome to Northrend, Death Knight. Now's when the real fun begins. We'll see you in Icecrown Glacier.