Hi David
Yes Canterbury is in NSW. It is on the outskirts of Sydney. Not sure exactly where as i am not from Sydney.
Had a look at
www.bdm.nsw.gov.au and did a search on Edna Smith as a bride and came up with over 9 pages of results. When i narrowed it down to just the district of Canterbury i got 6 results. I don't know if any of them would be your
Edna as it does not list parents names.
Once you have narrowed down the possibles you can order the certificate through the site. Certificates ordered through the site are A$24 at the moment but you can use a transcription agent which is cheaper .... there is a link on the site. Also a transcription agent can check details for you before you purchase the transcription.
Good luck
Jaki
PS Electoral rolls also might be the way to go. Not sure how to access them. Maybe someone else knows.