I thought at least some of the Australians might know the correct words, but apparently not.   Take it from a Scotsman this is the correct version, learned when I was a youngster (well over half a century ago!)-

Once a jolly swagman camped by a billabong
Under the shade of a coulibah tree
And he sang as he sat and waited while his billy boiled
"Who'll come a waltzin' matilda with me?"

Down came a jumbuck to drink by the billabong
Up jumped the swagman and grabbed it with glee
"You're a jolly jumbuck, you'll go in my tucker-bag
you'll come a waltzin' matilda with me".

Up rode a squatter mounted on his thoroughbred
Up rode the troopers, one, two, three.
"Where's that jolly jumbuck you've got in your tucker-bag
You'll come a waltzin' matilda with me".

Up jumped the swagman, leapt into the billabong
"You'll never take me alive!" said he.
And his ghost may be heard when you pass by the billabong,
"Who'll come a waltzin' matilda with me?"