DOZE: The verb "doze" is probably from a Scandinavian source; compare Old Norse dusa, "to doze."
These words are not actually pronounced the same, as the "s" in "dose" is pronounced as "s" (unvoiced), so "dose" does not rhyme with words like "rose" or "those." Notice also has the word "close" can be pronounced either way: "close" is an adjective meaning nearby when pronounced with an "s" sound, but "close" is a verb meaning to shut when pronounced with a "z" sound. English pronunciation: it's mind-boggling, isn't it?