Sadly, no... I'd be doomed!
Without getting political, my government would prefer it for me to face off against the Zombies with a sharpened piece of Mango...
Actually... speaking of Australian Survival chances, I'd probably make a beeline for Steve Irwin's Crocodile Farm. I'd have to dispose of Steve, on the suspicion that he may be a Zombie (I'm not convinced otherwize), but I'd set up a hideout in the middle of his crocodile farm/swamps. The slow-moving Zombies would be easy pickings for the hungry crocs, while I sit back and smoke a cigar.