I think in NSW one week of notice of the AGM is required (Seems very little to me. In the ACT it is 2 weeks or 3 weeks if there are motions for unopposed or unanimous resolutions to be put). However, to calculate the correct timetable for giving notices, reference has to be made to the Interpretations Act 1987 (NSW). When sent by post in Australia, notices are deemed to be received on the 4th working day after the letter is posted. Weekends and public holidays are not working days.
So, if posted on Monday 13th as claimed, the mail would be deemed to have been received on Friday 17th. Add a week and that makes Monday 27th the earliest possible date for the meeting. I think it might be within the letter of the law but it is extremely poor form to deliberately give only the minimum notice, unless there is some urgent decision needed as soon as can possibly be arranged.
Now that more than a further week has elapsed and you and perhaps others have not received the notice that was supposedly posted, I would start knocking on doors and collecting dated signatures from people who say they did not receive their notice. Your document could also allow for people to state when they did receive their notice, and if they did, whether the envelope was date stamped and, if so, what that date was if they still have the envelope. You might be able to prove that the manager and chair have lied about proper notice.