When I got my first Death Knight, on Blade’s Edge (EU) at the time, it was something of an experience.
First, we had to level some character up to 55. It was without heirlooms, and without the overpower we have today, so it implicated a lot of deaths. You had to have a character up to 55 before you could make one, and one only, Death Knight on the server where you had this character. And not on any other.
Then Blizzard removed this, on patch 3.0.8 (January 21st, 2009) so if you just had one character up to 55, you could make one, and one only, Death Knight on every server you liked.
However, with a bit of inventiveness, you can make as many Death Knight on one realm as you wish. You can make a Death Knight on any realm and then move this Death Knight to the realm of your choice, hereby obtaining extra Death Knights (as many as you wish).
Of course, you will have to pay for this, unless it is under the Free Character Migration program.
I had some Hordes on Draenor (EU) and really, I don’t like this realm. Then, it was possible to move for free from Draenor to different other realms (I chose Arathor (EU)). I started to make a Death Knight on this new realm, before I moved my characters and then I moved them. You can keep on doing it: Make a new Death Knight on one server and move her (or him) when you want, for free.
There are multiple advantages to that (aside from the fact that I like this class), Death Knight are born at level 55, 58 or 59 when they get out of “school”, they have gold, and they can very quickly quest and get professions. When this is done, only your imagination is the limit: Do you want to keep them there? Or do you want to move one of them loaded with gold and stuff to another realm? Everything is possible.
The only thing you have to do is to keep an eye on the free character migration possibility. Just write: Free character migration in the search field and get going.