Sarah The marriage in Sydney of Noel to Mary V. Burke is 1925. No birth indexes are available in any state of Australia after c1918. Still can't find anything on Noel's birth. A possible for Mary V. Burke in NSWis 1890/32736 at St Peters with father as Walter G. Burke and mother Mary A.
My suggestion would be to purchase the marriage certificate of Noel and Mary as it would have places of birth and parentage etc. The cheapest way is to use a transcription agent. [ think they're still listed on the NSW BDM site]