The following is from the Oxford English Dictionary. Its first use apparently can be traced to a Merrie Melodies cartoon of 1943. But its origin isn't really explained.
Expressing inarticulacy or incomprehension. Also (usu. mildly derogatory): implying that another person has said something foolish or extremely obvious.
1943 Merrie Melodies (animated cartoon) in J. E. Lighter Hist. Dict. Amer. Slang (1994) I. 672/1 Duh.‥ Well, he can't outsmart me, 'cause I'm a moron.
1963 N.Y. Times Mag. 24 Nov. 54/2 A favorite expression is ‘duh’.‥ This is the standard retort used when someone makes a conversational contribution bordering on the banal. For example, the first child says,‘The Russians were first in space.’ Unimpressed, the second child replies (or rather grunts), ‘Duh’.
1978 Washington Post (Nexis) 20 Aug. b1 A sergeant was standing there talking to the girl who's [sic] car had been hit, trying to calm her down. All of a sudden a city officer pulls up and he walks over to the girl, puts his arm around her shoulder and walks away with her. My sergeant was just left standing there, like, ‘duh’.
1990 J. Burchill in Sex & Sensibility (1992) 216 Ten years later, her intellectual and social betters aren't laughing any more but staggering around like punchdrunk fighters. Duh‥what hit us?
1998 Arizona Republic 7 May ev6 One reader asked why undercover police officers are running around with automatic weapons. Duh. Because the criminals have them!