I don't know if this is an "old" girl scout song, but my daughter's Brownie troop learned it from an official in our local council. I have the impression that she (i.e. the official) learned it in her girlhood. She insists on calling it "The Alligator Song", though you will see that it never mentions alligators. Here it is (with the possibility of a few mis-remembered words):

She sailed away, on a sunny summer's day,
on the back of a crocodile.

"You see", said she, "he's as tame as tame can be",
"I'll ride him down the Nile".

The croc winked his eye, as she waved her friends goodbye,
wearing a happy smile.

At the end of her ride, the lady was inside,
and the smile was on the crocodile.


Don