A little further comment:
s7.2 of CASA AC 21-41(0) states "...LSA are Australian aircraft as defined under the Act...", which is essentially what
KRviator quoted while I was typing earlier. Note the Civil Aviation Act 1988 is not the same as various regulations that may ensue from it.
Although it may not necessarily be the case here, in the event of things that are not defined in legislation the Courts will often refer to the meaning of a word from the Oxford English Dictionary. That august book states that a 'register' can be "
An official list or record of names or items.".
Thus, even if it's not defined in your Act or CAR's etc, I suggest there's little doubt on what it means - from which I would take the RAAus records to be a register of Australian aircraft (for the purpose of CAO 20.16.3).