No US president known as baby duck to my knowledge. A recent president of Haiti was called "Baby Doc".
baby doc
"Papa Doc" refers to François Duvalier, who served as the President of Haiti from 1957 until his death in 1971. His son, "Baby Doc," is Jean-Claude Duvalier, who took over the presidency after his father's death and ruled from 1971 until he was ousted in 1986. Both are known for their authoritarian regimes and human rights abuses in Haiti.
Duvalier was a former Doctor (Doc) and he's taking care of people like a father (Papa in creole) will do. So they call him : PAPA DOC. His son Jean-Claude, who will be the next president was called : Baby Doc
Here is a partial quote from an article in the Christian Science Monitor that I think explains it. "Baby Doc" Duvalier became the successor to the regime in 1971 when at the age of 19 he took over from his father, "Papa Doc" François Duvalier (indeed, he started off as a physician). As the following five slides attest, Baby Doc's infamy precedes him. - Stephen Kurczy, Staff writer I guess since his father was know as the "Papa Doc", it only befitting that he be called, "Baby Doc".
Doc - 1975 And Baby Makes Eight 1-16 was released on: USA: 3 January 1976
Papa Doc Duvalier
The Little Couple - 2009 Three Shops and a Baby Doc 2-16 is rated/received certificates of: Netherlands:AL
The Little Couple - 2009 Three Shops and a Baby Doc 2-16 was released on: USA: 9 February 2010
Your baby will arrive when he/she is ready to arrive
http://www.scribd.com/doc/7175163/Philippine-Presidents
Francois Duvalier. Also Known As Papa Doc!