It may be difficult to locate them, privacy laws in Australia mean that very few records are available inside of the last 100 years. I have the Victorian marriage indexes up to December 1945 and she is not showing there. I had a look in the newspapers too but didn't spot her. You may have a better idea of keywords to search for, so here is the link to the papers:
http://trove.nla.gov.au/newspaper
There are eight Edna Hendersons listed in the Victorian electoral roll in 1946, about double that for NSW and six in Queensland. I didn't check the other states. There are several Ellen Elizabeth Hendersons and two Elizabeth Ellen Hendersons but nearly all were Home Duties and none were with an Edna. The electoral roll does not give ages.
I used Findmypast to look for the electoral rolls which is free this weekend so if you wish to look there you could. If you know what Edna did for a living you may find her here.
Cox and Henderson are both common names in Australia.
I'm not seeing much else, but take a look through Trove. It's a good resource, although for privacy reasons again there is not much digitized for recent decades. Also, if you think they might have passed away in a particular city, many cemeteries indexes are online but not in one place. Generally this is a service by the cemetery authority so if you know the town you can find their website. Melbourne has a very good one if you think they might have stayed in the city:
http://mgc.smct.org.au/deceased-search-help/
With a bit of fossicking you might find something. Trove might get you to a town or suburb, after which you can use electoral rolls and cemetery records.
Also, each state of Australia looks after their own records and which records are kept can be different state by state, so you need to work out the state they lived in to take the next step. Just because a particular year is the cutoff for public records in one state, doesn't mean that it will be the same in another.