(paper has a typo saying 1951, then goes on to refer to the Sixties script).
1951 is correct. There are show timelines
here and
here. It started in '51 and ended in 1960, but the cast was reunited a few times in the '60s, so the joke was recycled in the '60s script. There are some very short audio clips at the second link.
The Independent's story says:
QUOTE
A study of rare footage from 1951 showing the Goons in their first television appearance has an early version of the joke performed by Milligan's fellow Goons Michael Bentine and Peter Sellers.
The Independent story also mentions this joke supposedly favoured by scientists:
A man walking down the street sees another man with a very big dog. One man says to the other: "Does your dog bite?" The man replies: " No my dog doesn't." The man pats the dog, which bites his hand: "I thought you said your dog didn't bite," said the injured man. " That's not my dog," replied the other.
Peter Sellars, one of the Goons, used that joke in a Pink Panther movie, making me wonder whether Spike Mulligan wrote it, too.
I'd add more links, but the wick in the engine has gone out.