Green’s Dictionary of Slang

to accomplish something easily, e.g. win a race.

1937		R. Westerby Wide Boys Never Work (1938) 119: Watch him doddle home.
1963		J. Winton Never Go to Sea in Partridge DSUE (1984) 322/1: I think she [i.e. a filly] started at even money, but anyway she doddled it.
1973		T. Lewis Billy Rags [ebook] A nickful of them [i.e. criminals] and no one had doddled.