That registration number should be correct.
Edited to add: Sorry, I'm not quite awake this morning ;-)
"Birth and change of name records are restricted from public access for 100 years or until the person has passed away, whichever is the later"
The Digger Great War Index was published prior to the introduction of the 100 year rule.
Check out the VIC BDM Access Policy. I know children can apply for their parent's birth certificate if they are listed on the parent's death certificate, but not sure about grandchildren.