In order to be able to create a Demon Hunter, you need to have at least one level 70+ character on that server. In contrast to Death Knights, which are unlocked to all servers once you reach level 70, the Demon Hunter acts on a server basis, so you cannot create one on a fresh server.
There is however a trick to be able to create a Demon Hunter without having a level 70+ character on that server. You need to have Legion, because this lets you create a Class Trail Character. These will be level 100, and does not really count to unlock the Demon Hunter, but if you are fast enough, you will be able to do it. So create a Class Trail Character and click on the button to create a new character asap once it's level 100. This will have Demon Hunter as an unlocked option most times, but if it does not work, delete the Class Trail Character and try again. You can create 5 of these per hour, and you will most likely be able to get the Demon Hunter easily within these 5 tries.