Very little of Dorium's background is given out on screen. All we really know about him is he owned his own interspace bar on a moon or asteroid, owes the Doctor a favor from a long time ago (possibly from when he was younger and skinnier, depending on how you interpret his words), he's possibly from the 51st century, and he has excellent connections.
If I had to guess his race, I would say it would be "Blue Human". No, I'm not joking. In Tennant's run, we briefly see races of humans that have, red, white, and blue skin. There is no special mention given to these humans on screen, but there are mentioned in the TARDIS wiki. As far as I can tell, there is nothing notable about these races than the colors of their skin.
Sorry I couldn't be of more help, but that's all I've got.
On the other hand, among the trailers on YouTube about the BBC's 50th anniversary event, there is a scene with the severed head of Dorium Maldovar (see "A Good Man Goes to War") still talking. That seems a little bit far from near human.
As I understand it, Dorium is only still alive due to the Monks' intervention. For some reason, they prefer their members stay living after their beheading. I don't think his head still living and talking is an inherent property of his species.
I would say if you wanted to stat up the Blue Humans, I'd give them the Alien Trait(Special Good), and Alien Appearance (Minor Bad). Besides that, their states would be fairly normal.