The quickest and least practical method is to let it bite you.
If it bites you and you die, it was poisonous. The almost equally dangerous method is one presented to me by my
freshman geography teacher, who has travelled the entire world and knows pretty much
everything.
He and his friend were driving way out in the middle of Australia and stopped along the road for a short rest. His friend says "Hey, I wonder if that snake's poisonous..." He proceeded to pick up the snake by the tail, wait a few seconds, then announce "Yep, it's poisonous, alright."
My teacher was quite impressed.
His friend then twirled the snake about his head and cracked it like a whip, causing the head to fly off, but that's a different story.
OK, kids, here's how it works. If the snake is poisonous, its head will be too heavy to reach up and bite you whilst you have it by the tail. If it is non-poisonous, there is a good chance that the head will be light enough for the snake to bite you. Sure, it'll hurt, but at least you won't be dying the death...
People, never, ever, ever try this. As far as my teacher knows, this only applies to Australia anyway, but don't try it there, either.
Ah, but there is a third method here. Consider the world's most venomous snakes. Now consider how many of them live in Australia. If you haven't made the connection yet, my point is to treat any snake (Australian or otherwise) as if it were poisonous unless you have some sort of semi-professional qualified snake handler with you. This is obviously the safest method.