As W. Labov has passed away, I came across a comment reposting this screenshotted request, along with the paper in question:
https://betsysneller.github.io/pdfs/Labov1966-Rabbit.pdf
The paper is quite a rollercoaster, ranging from describing of disturbingly racist ideas about native Hawaiian and Black children that some scientists still pushed at the time (1970!*), to Labov's own disarmingly cute and humane solution to the issue of testing children's language abilities.
Edit: *1970 - according to the article itself, which is apparently based on Labov's 1970 talk; however, the URL suggests that the article was published in 1966, which is contradictory. I'll try to find out where and when this was actually published...
Edit 2: It looks like it is from 1970, from Working Papers in Communication, vol. 1 (Honolulu: Pacific Speech Association). It is surprising that a recently published book also claims that it's from 1966, probably the authors got the file from the same URL with the wrong year.
Edit 3: The original Twitter thread: https://xcancel.com/betsysneller/status/1516848959284678656
A little 6 year-old boy doesn't talk.
His Mother takes him to the doctor, who says, "He's fine. Just give him time."
A couple months later, his Mother takes him to a Child Psychologist, who says, "He's fine. Just give him time."
A couple months later, his Mother is cooking his breakfast and she accidentally burns his toast.
Scraping the burnt toast over the sink, She thinks to herself, "He'll never know the difference", and she serves the toast.
As she turns back to the sink, the little boy says,"This damn toast is burnt!"
Shocked, the Mother turns and says,"What did you say?"
"This damn toast is burnt!"
She says,"Omigod! You're talking! What happened? Why did you take so long to talk?"
"Up till now, everything was OK."