Interestingly, the liner notes to the Louise Bennett album give a different explanation for the song and print slightly different lyrics. "A red-headed Negro girl is told why her hair is red and is warned about losing her boy-fried, who does not like the colour of her hair."
Here are those lyrics.
Lyr Add: CUDELIA BROWN (from Louise Bennett 1954, "Jamaican Folk Songs")

1. Oh Cudelia Brown,
Wha meck yuh head so red?
Oh Cudelia Brown,
Wha meck yuh head so red?

Yuh siddung eena de sunshine,
Wid nutten' pon yuh head,
Oh Cudelia Brown,
Dat's why yuh head so red!

On a moonshine night, on a moonshine night,
I meet Missa Ivan, an' Missa Ivan tol' me,
Sey dat him gi Neita de drop,
Jamaica flop, an' de moonshine drop,
And the reason why, because
Her head so red & (etc.)