Yes it was but it wasn't celebrated as a Public Holiday until 1994
Just checked your claim and found a column in The Argus dated 26th January 1935.
Seems that the first unison of States celebrating the day was because of an agreement the previous year.
So it's likely that the date came first and the citizenship act chose that date to come into effect.
The article states the reason for selection of the date is Sydneycentric. https://trove.nla.gov.au/newspaper/article/11010528
