Significant periods in the Churches history in Australia By abbie.ewens 1788 La Perouse enters Botany Bay and his chaplain, Abbe Mones, celebrates the first Mass within Australian territory 1791 First Irish convicts transported to Botany Bay 1803 First official public mass 1819 Father John Therry and Father Phiip Conolly arrive in Sydney as Australia's first ever priests. 1825 Father Therry removed from his role of the colonys official chaplin.