The man pleaded guilty to unlawfully possessing a firearm and an imitation firearm following the unusual episode on December 28.
Driving through a car park near Smails Beach, Meldrum pointed a fake pistol out of the window at two people in a parked car.
After waving the plastic gun at them for a few seconds, the defendants circled the area and returned.
The younger man got out and pulled a long-barrelled air rifle, that he had bought earlier that day, from the back of the vehicle.
He then loaded it in full view of the victims, who quickly fled the scene and contacted police.
Carrying the weapons and cans of Bourbon and Cola, the defendants wandered on to the beach.
When officers arrived they found Meldrum holding a "recently deceased" duck, and with an imitation pistol in his jacket pocket.
Counsel Brian Kilkelly said his client's intoxication was at such a level, he barely remembered the events of the evening.
"These were the actions — and these are my words — of two real dumbos," he said.
"It was an absolutely appalling, but drunken, episode."
While on bail, on March 1, Meldrum came home drunk then pushed his mother when she blocked his path, resulting in an additional assault charge.
Kilkelly said the defendant was surrounded by friends and family who, like him, struggled with addiction.
"Any alcohol for him is too much. He needs abstinence to be part of his daily routine," he said.
Judge Large stressed that Meldrum was on the cusp of imprisonment.
"Firearms are dangerous enough in the hands of sober people, let alone drunk people," he said.
As well as the rehabilitative sentence, the judge also imposed 120 hours' community work.
