There may be a real-world example on Quora from Don Grushkin, Professor of Deaf Studies (Ph.D. in Language, Reading and Culture).
I've added the bold.
I'm not sure anybody's ever conducted any research on rate of linguistic drift. As Joachim Pense notes, languages can be created in one or two generations. But you're talking about linguistic change from one form, say, "Old English" to a newer form, say "New English".
One example that we can look at to see linguistic drift occurring is in the case of American Sign Language. ASL was created in 1817, with the establishment of the American School for the Deaf, where French Sign Language was imported and likely blended with Martha's Vineyard Sign Language, and possibly some American Indian Signs, or some local Deaf community signs (there were a few Deaf communities emerging in the early NorthEastern United States).
In 1880, the use of signed language was officially banned within Deaf educational settings, and the language started to go underground, to some degree. In 1913, the National Association of the Deaf, fearing the death of signed language, commissioned a series of films (around 6 or 7 films) in order to preserve the history and the language. Most of these films survived today. You can watch one of these films here:
To modern signers of ASL, it is difficult to understand the signs (I can, but only because I've seen a translation and have watched the film many times). Our difficulty shows that the language has undergone a significant drift in about 100 years, or about 5 generations. This drift might have been accelerated by other factors such as invented signed systems, the banning of ASL in education (causing some areas to invent their own sign language or variation of ASL), and the lack of a written form of ASL.
Given a small, isolated community after a catastrophe, I think it is quite plausible to find a new, unintelligible language evolving in that short a time.