The Connie, VH-EAC, was written off in Mauritius in 1960, but noone was killed. But Qantas had some other write-offs earlier, before WW2. And the difficulty with such a statistics-operation; Qantas inherited and took over some other companies which DID have some (but not many) crashes. Like (Trans)Australian Airlines. So you can't say they have a PERFECT record.
America West had no real crashes but they declared a 737 N198AW a write-off, but that was because it was an oldie. If they knew they would be judged on it, they might have fixed it.
Other major airlines whitout crashes: Singapore Airlines, BWIA, Kuwait Airways (only loss are aircraft destroyed by Iraqi's), Tunis Air, Hawaiian Air, Monarch Airlines, Japan Transocean, Emirates Airlines, Royal Brunei, klm UK, Midway Airlines, American Trans Air, Air Malta, Transavia Holland, Aero Lloyd, PremiAir, Tower Air, Virgin and Meridiana.
But the real majors have just made too many flights in a time when accidents did happen ten times as much as now.
So in fact, airlines like Continental, SAS and BA have more impressive records than most of these smaller lucky airlines.
nobody has ever died from hard work, but why take the risk?