In most US states, drunkenness essentially substitutes for the mens rea necessary for general intent crimes (or, roughly, those requiring only "recklessness" as to the result of the crime) Since most statutes often called "involuntary manslaughter" are more properly called reckless manslaughter and not surprisingly usually have recklessness as the mens rea. You could charge him with reckless/involuntary manslaughter in most US states.
The problem in obtaining a conviction is causation, and that would really depend a lot on what state you're in. Generally, for you to be convicted of a crime involving recklessness, the way the crime/accident happens must be a harm within the risk of the recklessness. This would be a slam dunk if the girl had been sitting in another car; the problem is that you could easily claim that either the recklessness wasn't the cause (that is, any driver, even a non-reckless one would have hit the girl) or that the way this went down is so weird as to not be a foreseeable result of the recklessness imparted by being drunk (that is, when you get drunk and drive, you're taking the risk of hitting parked cars, other driving cars, pedestrians crossing the street, but NOT people lying in the street, since that's totally unforeseeable). There's also an issue of the girl being an intervening actor.
That all said, I have no idea about Aussie criminal law. It may be (but is not likely) radically different.