dumb - old english, of germanic origin, related to old norse "dumbr" and gothic "dumbs" - "mute"; also to dutch "dom" - "stupid", and german "dumm" - "stupid"
dummy - from late 16th century, dumb+y. the original sense was [a person who cannot speak], then [an imaginary fourth player in whist] (mid 18th cent). whence [a substitute for the real thing] and [a model of a human being] (mid 19th cent)
so, i guess it was originally dumby. probably just one of those words that morphed over time, like how words like "ain't" came to be.