It's good to write "a southern accent". It has been pointed out in several replies that there is no one Southern Accent, and it has changed over time.

Mentioning previous answers is intended to provide quick pointers to existing answers, not to discourage further questions. If you have more questions or disputes, please feel free to post them.

A recent answer by /u/YuunofYork , a linguist, was in "How close was George Washington's accent to the modern American accent?" under https://www.reddit.com/r/AskHistorians/comments/7w4ldq/how_close_was_george_washingtons_accent_to_the/ . It does look a bit at Washington in particular, but just to aver ignorance about Westmooreland, Virginia, and "Washington was a 4th generation native Virginian, so we can assume his speech followed suit with his peers, but it's difficult to say with certainty what features his peers had for several important reasons". So they mostly talk about what features might or might not have existed then.

The FAQ has a section on English accents and dialects at https://www.reddit.com/r/AskHistorians/wiki/language#wiki_accents_and_dialects . Specifically:

Despite the title, in "How has the American Southern accent changed since the Civil War? Before the war, was it perceived as prestigious in the North and elsewhere?" at https://www.reddit.com/r/AskHistorians/comments/34pux1/how_has_the_american_southern_accent_changed/cqx5nsc/ , /u/tropical_chancer discussed pre-Civil War accents.

"What caused Americans to develop a different accent than the British?" at https://www.reddit.com/r/AskHistorians/comments/39i1k4/what_caused_americans_to_develop_a_different/cs4370z/ has a relatively short comment by /u/keyilan on the general phenomenon, and a link to a comment by chocolatepot.

"How did the "Southern" accent develop on the U.S and what accounts for its variation across the region?" at https://www.reddit.com/r/linguistics/comments/5xn77e/how_did_the_southern_accent_develop_on_the_us_and/ is a bit loosey-goosey, despite being only 11 months old, and it depends on links -- there's no good definite chunk to point to. But there's some Appalachian stuff, and zabulistan quotes their words about more recent Southern dialect development which may inform you of what you consider "a southern accent".

Speaking of all over the place, Thesleeperhold asked on /r/linguistics , with "How did the "Southern" accent develop on the U.S and what accounts for its variation across the region?" at https://www.reddit.com/r/linguistics/comments/5xn77e/how_did_the_southern_accent_develop_on_the_us_and/

And if you want some general philosophy (mostly addressing the premises), "Why do people in the Southern US have such strong accents?" at https://www.reddit.com/r/AskHistorians/comments/2euwlc/why_do_people_in_the_southern_us_have_such_strong/ , from citrusonic and Sev3rance.