Peter, Paul and Mary have the lyrics for a common version (copyrighted in 1952):
The popular version recorded by Burl Ives is slightly different,
featuring the last line, "She died, of course" instead of the more
upbeat "She's alive and well, of course!"
Here's a bit on the history of the song:
"Alan Mills, ebullient Canadian singer came across these these verses
in a magazine, changed them a bit, added a few more, and added a tune.
Countless, future generations of children will enjoy the result."
"burl ives" "she swallowed the cat to"
"alan mills" "she swallowed the cat to"
I hope this helps.