Order of events after the flood:
First, God confounded the languages. Second, He divided the continents via a continental shift.
We know that God had to first confound the languages before dividing the earth in the days of Peleg.
How do we know that the confusion of tongues had to come first?
We know because if God divided the continents first, then the people that were moved in the division of the land mass, would have all spoken the same language. Therefore, the natives living in South America, and the natives living in North America, and the Aborigines of Australia, and the Pacific Islanders, etc, etc, would all speak the same language. But they do not. In fact, there are hundreds of different languages in Papua New Guinea alone. And of course, the numerous languages are evidence of the confusion of tongues that took place at the tower of Babel.
So, God first confounded mankind's language. This confusion of tongues resulted in a natural diaspora. Chinese speaking people gathered together in one area. Maya speaking people in another, in the portion of land that would later break off and move across the sea until forming the continent of South America. And so on.
In all likelihood, God confounded the languages, or the tower of Babel incident occurred, in the days of Eber. Eber was the calendar reference patriarch that lived just prior to Peleg. Actually, Peleg was born the same year that Eber died. Roughly, about five thousand years ago. Exactly matching the time in which the earliest record of a known alphabetical language can be found.