"Dou-Dou" (pronounced "do do" is an Eastern Caribbean word meaning "sweetheart". In the context of that line, the English wrod "fair" means "(physically) attractive". Thus, in my opinion, the line "I met a duo dou fair" means "I met an attractive beautiful (or handsome if the gender is male) sweetheart." And I believe that the line "darling do do" means "darling sweetheart"

See this book review that includes information about this term
(I think this review is interesting in its own right)

Maureen Warner-Lewis
Launch of Curdella Forbes' A Permanent Freedom, Leeds: Peepal Tree Press, 2008, 195 pp.
The Undercroft, University of the West Indies, Mona
9th February 2009

..."The Jamaican grandmother of the technically accomplished story called "Say", speaks Jamaican Creole, but interlards it with the Eastern Caribbean word 'dou-dou' meaning 'sweetheart'. Her grand-daughter's father is from St. Lucia."

-snip-

http://dictionary.sensagent.com/doudou/fr-fr/ indicates that "dou dou" is a French term that means "ma cherie":

"definitions Magnifique,doudou ourson, de marque Comptine (1.0 EUR)
Commercial use of this term

doudou (n.f.)1.(familier)ma chérie, aux Antilles."

-snip-

And since this is a folk music forum, see this use of the term
"Dou Dou" as an add-on to a person's name (perhaps like "Honeyman" or "Honeyboy")

Dou Dou N'Diaye M'Bengue
Thiato Thiate
Dunya Records (www.felmay.it)

There is no doubting the origins of Dou Dou N'Diaye M'Bengue from the moment he begins to sing. Son of griot Bala Nar M'Bengue, and born in Dakar, this release is a collection of tracks by a singer steeped in the Senegalese traditions that have now become so familiar to us through the music of superstars Baaba Maal and Youssou N'Dour. Unlike a lot of his predecessors, Dou Dou here presents his songs and his voice in a simple, understated style, with minimal arrangement, accompaniment and instrumentation. He gives us a rare glimpse of what an authentic, village performance might sound like.

The outstanding song on the album, for me, is the title track, "Thiato Thiate". Extremely simple, with xalam, percussion and an underlying keyboard providing chordal support, it is immensely beautiful. The singing is simultaneously powerful and subtle, with the repetition weaving a kind of magic over the listener. There is hardly a better vehicle for Dou Dou's voice, and the sincerity and sensibility which he brings to a song such as this is intensely moving"...

http://www.rootsworld.com/reviews/mbengue.shtml

-snip-

I should also note Google hits also suggest that "Dou Dou" is a Chinese name or nickname, but that's a whole 'nuther etymology than the Caribbean use of the French term "dou dou".