The Dark Iron Core Hound is a mount with a unique skin that is only obtainable by alliance characters. In order to get it you will need to complete the Dark Iron Dwarves recruitment scenario. Upon completing it, you will get this mount that can be used by all your Alliance characters, as well as the ability to create a new Dark Iron Dwarf character on your account.
The recruitment scenario is actually pretty short, so it should not take you too long to complete with a max level character.
There are most likely some requirements you need to complete before you can begin the scenario, but these are not currently known, so we will update this post once it's announced. It seems likely that you need to be level 120, and possible have some reputation requirements as well.