Hi Alamo,
You are correct that Australia refused to allow any of its men to be executed. This was due to an incident during the Boer War when two Australian Officers ("Breaker" Morant and Peter Handcock) were executed without the Australian authorities being consulted.
Unfortunately New Zealand did not follow suit and five NZers were executed during WW1.
From NZ History website : "28 members of the NZEF (were) sentenced to death during the war. Five of these men, all privates, faced a firing squad: John Braithwaite, Frank Hughes, John King, Victor Spencer and John Sweeney. Four were executed for desertion, Braithwaite for mutiny.
In September 2000 all five men received posthumous pardons when the New Zealand Parliament passed the Pardon for Soldiers of the Great War Act."