Given the time it took to get all men back to Australia and the complications of the 'flu epidemic, the booklet may not have been published until late 1919-early 1920.
The National Library of Australia is currently undertaking a project to digitise old Australian newspapers - they are scanned and 'translated' using OCR technology. Given the varying qualities of the print, the 'translations' are a bit iffy, sometimes useless, but anyone can sign in as a guest and make corrections.
Definitely worth looking up your WW1 soldiers - injury and death reports, In Memoriams, etc. can often be found.
As far as the booklet is concerned, I did wonder if it was included as a Supplement, but haven't managed to find it yet. I have, however, found the report of a dinner given at the Burlington for returned staff of the Sydney Morning Herald and the Sydney Mail published in Sydney Morning Herald on 3 May, 1920. This article contains a reference to the booklet - so it was obviously published prior to that date. See
http://newspapers.nla.gov.au/ndp/del/article/15887971?searchTerm=fairfax+served+war for the article.
I suggest you contact SMH Archives by letter or email and ask them is they can supply a copy. In the meantime, you might like to search the NLA site yourself.
Barbara