Maybe the pup reminded him of home, a safer place where people kept pets. Or maybe the pup had enough personality to con Moody to take him back to camp.
Either way, the little dog and the little Digger were soon inseparable.
It was Egypt, 1940. Moody was a despatch rider with the 2/1 Machine Gun Battalion in the desert war. The soldiers weren't supposed to take in strays as pets but for Moody's crew, rules were for bending.
Moody wasn't overawed by officers. He was nearly 30, originally came from Brighton and had coxed a rowing crew at Scotch College. He'd been a jackaroo before the war and had knocked around a lot. The little dog should have been called Lucky but for some now-forgotten reason they called him Horrie.
He trotted beside the troops on marches and followed the commanding officer on parade. When they went to Greece, Horrie travelled in Moody's kitbag.
But it wasn't all one way. Horrie wasn't big but he pulled his weight. People facing the risk of death seize on anything that might help them survive. Horrie's acute hearing meant he could hear approaching enemy aircraft before the men could. He was a four-legged, biscuit-stealing, leg-cocking, tail-wagging, early-warning system.
He was wounded with shrapnel during the evacuation of Crete. When snow fell in Palestine, the Diggers made him a coat from an army blanket, complete with regimental colours. In all, he survived five campaigns against Hitler's troops.
With every passing month, the bond between man and dog grew stronger.When the battalion returned to Australia to face the Japanese threat, Moody ignored orders that no animals be taken as a precaution against diseases - especially the incurable killer, rabies.
He had Horrie checked by a vet in Tel Aviv to make sure he was healthy. Then he modified his pack, stiffening it with plywood and cutting air vents, hidden by his helmet.
On the troop ship home Moody or one of his mates stayed with Horrie below decks at all times, ready to hide him if there was a search. They trained him to lie still under blankets and secretly fed him and disposed of his droppings.
For the soldiers' pets, the risk of discovery and instant death was real. One troop ship reputedly stopped for 12 hours off Fremantle until soldiers finally surrendered a cat. Military police flung the unfortunate pet overboard before the ship could dock.
But Horrie survived. Moody smuggled him off the ship in Adelaide and left him with his father in Melbourne, while he served in New Guinea.
After Moody was discharged in 1945, he took Horrie to Sydney, which is where the story might have ended if he'd kept the secret among family and friends. He assumed that three years was long enough for the quarantine laws to lose their edge, but he was wrong.
When he offered to lend Horrie to the Kennel Club to raise funds for the Red Cross, officials were stung into action.
Keen to discourage other returning servicemen from trying the same trick, they ordered Moody to surrender his dog to be shot, despite expert advice by the Government's own experts that the dog presented no threat of disease.
Moody fought for time, telling the officials the dog was in Melbourne and would have to be brought to Sydney. Official approval of this arrangement showed how little the dog was considered a real health risk. Quarantine officers seized the little white dog Moody produced. It was shot in March 1945.
The public was outraged. Angry dog lovers wrote letters to newspapers, politicians and the Quarantine department, which actually sought legal advice about suing one letter-writer for "defaming" unnamed public servants.
Cartoonists lampooned officialdom, one depicting Horrie as a blindfolded prisoner of war being shot by firing squad.
The first of many wreaths in Horrie's memory was laid on Anzac Day at the Sydney Cenotaph.
Nearly 60 years later, Canberra author Anthony Hill was planning to include a short chapter on Horrie in a collection about Animals at War. He was at a book launch in 2002 when a veteran journalist, Norma Allen, quietly asked if he wanted to know the real story of Horrie's fate.
She told the intrigued Hill that as a teenage reporter in 1946, she had interviewed Jim Moody. She said when she had sympathised about Horrie being put down, he told her a secret she would keep most of her life: Moody had searched dog pounds for another white terrier to hand in to be shot, and bought one "for five bob".
Meanwhile, the real Horrie had been smuggled one last time - to a farm in the Corryong district, he hinted.There, the story goes, Horrie sired many litters of pups, so no one would be able to pick which one was him.
Hill traced Jim Moody's widow, children and close friends and confirmed the family secret. It seemed Horrie had lived happily ever after. But his master didn't.
Norma Allen never forgot what he told her: "You don't think an Australian soldier would leave his mate behind, do you?"
Moody's family are proud of the story of their maverick forebear saving his little dog. But one question teases them: are any of Horrie's descendants out there?
Source: ANDREW RULE, HERALD SUN, APRIL 18, 2013