A fairly basic question I suppose, but who actually assigned
  original control of AU-DOM to kre?  Where do the top level
  domain holders derive their authority from?

THE IANA. Jon Postel delegated immediately below "."

because ACSnet existed, and .oz existed as the first widely dispersed
network, and because munnari was functioning as a the global interconnect
to talk to uunet, and eventually (immediately pre-AARNET) had the first
IP connectivity to the USA with wider reach (csiro-dit had access for instance)
the delegation made sense. 

	Kre would have been the first DNS-on-global-internet active node
	of any size and repute

	Kre already acted as mail mail forwarder for most of australia

	there was no ISOC or other chain of command, it was IAB/IANA and
	thats about it.

My view. Could be wrong.

-George