@Grant
Darwin (and the Top End in general) used to have very distinctive slang (gammon (or gammin), budju, grouse, gash etc), but it'd pretty much died out by the late 90's, early 2000s.
Keep in mind my story is set in 1984 / 85. (Finally made it there!)
While you don't use it NOW, what about then?
And yes, I've heard sprog used before regarding children.
The person saying this specifically is an indigenous Australian, is from the NT, and specifically near Uluru. I realize that with the size of Australia, just as in America, the place is so big that what someone says on the east coast isn't what someone says on the west coast.
ETA: I also realize that a lot of Australian slang has British roots, because of being a Commonwealth nation.