Jenkins killed the dog eight hours after the attack, disappointed at what he perceived as a lack of action by police.
But the court heard police had indicated to Jenkins they would remove the dog from the general population, Fairfax reported.
That prompted him to collect the dog from a woman caring for the dog, whose owner was away receiving cancer treatment.
Jenkins lawyer Brett Daniell-Smith said his client, who was suffering severe depression and financial troubles while facing terminal cancer, when the attack occurred had shown remorse for his actions.
Crown prosecutor Ruth Thomas emphasised the "premeditated nature" of the stabbing and asked for a short jail sentence, Fairfax reported.
Judge Bill Wilson said that would be "inappropriate".
"There must be a difference between wilful ill-treatment of an animal and a misguided attempt to dispatch an animal that in your mind had lost its right to live."