There has been research done on this subject.
The Qualls Concise English Grammar claims that:
"The Appalachian dialect is the oldest of English dialects in British
This source focuses on populations exceeding 2 million so it includes groups from the USA, Canada, and Jamaica. It is also interesting to note that Qualls believes that several of the the North American dialects are the oldest in the world, in that they retain so many elements of 16th century usage.
If I wanted, I could post other sources that support other regions like Newfoundland being the oldest dialect in North America (and I mean including everything north of of South America).
I could further then get into to the debate of whether the North American dialects are really oldest, and could argue a dialect like that from the Newcastle-upon-Tyne area ('Geordie' accent) is even older since it retains so many elements from the 5th century, as this blog claims.
But I don't think that Qualls or the blog about the Geordie accent or any other source I might cite that would argue a different dialect being oldest is correct. I prefer the description given by this Brief History of the English Language.
Also significant beginning around 1600 AD was the English colonization
of North America and the subsequent creation of American English. Some
pronunciations and usages "froze" when they reached the American
shore. In certain respects, some varieties of American English are
closer to the English of Shakespeare than modern Standard English
('English English' or as it is often incorrectly termed 'British
English') is. Some "Americanisms" are actually originally English
English expressions that were preserved in the colonies while lost at
home (e.g., fall as a synonym for autumn, trash for rubbish, and loan
as a verb instead of lend).
The American dialect also served as the route of introduction for many
native American words into the English language. Most often, these
were place names like Mississippi, Roanoke, and Iowa. Indian-sounding
names like Idaho were sometimes created that had no native-American
roots. But, names for other things besides places were also common.
Raccoon, tomato, canoe, barbecue, savanna, and hickory have native
American roots, although in many cases the original Indian words were
mangled almost beyond recognition.
Spanish has also been great influence on American English. Mustang,
canyon, ranch, stampede, and vigilante are all examples of Spanish
words that made their way into English through the settlement of the
A lesser number of words have entered American English from French and
West African languages.
For any of the varieties and dialects that exist in North America, some (like Qualls) may try to argue that because certain historical words persist in that dialect, that the dialect is older, but what no one can deny is that all English dialects around the world include many newer words which have been introduced to the language over time, and these newer words are spoken side-by-side with the older words, so none of the dialects is really the same as was spoken in historical times.
If interested in further investigation, this source provides a lot of current information on North American dialects in the USA and Canada, in how they differ and where they are located, but not so much their date of origin.