I've done a little bit of research into the song myself, and I may be able to fill in some of the gaps:

1. when introducing the song on his 1954 "Coronation Concert" album, Burl Ives says that he learned it in Florida and that it references a paddleboat called The Cherokee.

2. doing some Googling, I found a ship called The Cherokee that was indeed associated with the St. Johns River -- but it's an ocean-going steamship, not a river paddleboat! (link)

3. The earliest version I've found is by Burl Ives, on his 1950 album "More Folksongs". (link) It was also released on a 78 in 1950 (link). It was reportedly recorded in February 1950 and originally credited as "Trad."

4. according to this website, Dinah Washington's version was recorded in September 1951. If true, then it must not be the earliest version. Also, it's worth noting that Washington's original single (link) credits the song's writer as just "Lee".

5. Speaking of "Lee", I found a 1959 version by someone named Katie Lee (link) which contains the same "Lee, Ecton" writing credit that would later be associated with the song. But where did "Ecton" come from?

6. many of you are probably familiar with Erik Darling's 1961 version of the song (link), but what isn't as well known is that Darling also played guitar on the 1965 version by Lisa Kindred. (link)

7. Lisa Kindred's version was the inspiration for Quicksilver Messenger Service's 1967 song "Babe I'm Gonna Leave You". (link)

Anyway, I can't find any evidence of the song prior to 1950, but it seems reasonable that it was indeed a traditional song native to the Florida area.

I hope that was helpful!