The early part of leveling the Death Knight is both fun and incredibly rewarding in terms of lewt. Compare the experience to what you have to go through to play any other class and you’ll agree that the early DK levels are fantastic and way more enjoyable than even the first 20-40 levels of most character classes.
You are going to start by doing a bunch of quests for the Lich King. The early quests should take your Death Knight from level 55 to abot 58 or so. You’ll get an epic mount and loads of talent points. If you are unsure how you should spec your DK for leveling up to 80, I suggest Unholy. WoW Insider has a fantastic rundown on a good solo Death Knight spec. The only thing I would change is to make sure you drop 2 points into the “On A Pale Horse”. That skill will save you hours in leveling.
The other thing you want to make sure you do is install the QuestHelper mod. QuestHelper is a huge time saver as well. It keeps you pointed in the right direction, so you can run through quests a ton faster and get XP a lot faster.
If you are thinking about getting a profession, I would just wait until you hit level 80. The Death Knight gets ton of gold to start out the game and has plenty of great armor to start with, so you’ll be able to run up to level 60 or 62 without having to buy really any armor or weapons, just your skills, which is nice. If you feel like you need gold, you should try Luke’s Gold Guide or Warcraft Tycoon. Both guides will help you get a lot of gold via an alt without slowing down your leveling.
Once you hit level 58, you should skip right into the Outlands and start running the Burning Crusade content. The first BC zone will get you to level 62 or 63. Just run all the quests you can until you just have the group ones left. Once you get that far along, you should be level 62 or maybe 63, then you should move into the next zone.
That’s it for the early DK levels. It’s a fun character class and before you know it you’ll be through the Outlands and into the Wrath of The Lich King content again. Good Luck!