Choosing a profession (for any class, not just Death Knights) means that you first have to choose your goals. So ask yourself question #1 first: What do you want out of a profession? Gold, or stuff for yourself?
If you want gold, the answer is easy. Choose gathering skills and sell mats used by crafting professions. Some crafting skills can be very much like gathering skills - Enchanting is what comes to mind (Disenchanting). You might also want to add in fishing (mats for cooking) in as a gathering skill.
If you want to choose a profession for the stuff it provides your class, do it without any expectation of making gold from it. If you do end up making gold (unlikely, but there are exceptions), count it as a blessing that may go away at any moment, when others discover your niche.
When choosing a profession to make stuff, the first thing you do is eliminate any profession that makes stuff not applicable to your class. This is mostly in the armor-making areas. After all, as a Death Knight, you really have no use for Tailoring or Leatherworking. That leaves a bunch, so let's look at each (with the associated gathering skill) individually. Doing your own gathering will slow production, but has the benefit of being a lot cheaper than buying the mats on the AH.
Alchemy/herbalism. You go through a lot of potions at end-game, and I'm not talking about healing or mana potions. One of the benefits is that you can build a client list from people who need more. On the other hand, you'll probably be under pressure to provide potions for free to your guild.
Blacksmithing/mining. Create your own armor and/or weapons. The titansteel recipes are extremely good, and Eternal belt buckles have the ability to add a gem slot to a belt.
Enchanting/no gathering skill. This profession can make you rich (disenchanting) or make you poor (power-leveling), depending on the speed you want to level the profession. An empty profession slot is a big plus. If you need to purchase mats for the profession you choose for the slot, (DIS)enchanting can provide the gold.
Engineering/mining. The difference between men and boys... Engineering has some marvelous toys, and for the most part, that's what they are.
Jewelcrafting/mining(prospecting). Everyone needs gems, but the beauty of this profession is the stuff you can make for yourself that no other profession can equip.
Inscription/herbalism. Also something that everyone needs, but there are no returning customers. In general, once someone buys inscriptions, they don't need any more.