First of all, the proper ethics to pose these questions is first not to distort information because it then put your crediblity in question. Do you even know what wet-dream means. Where does it say that prophet (saw) had any wet-dream. And how did you conclude that she did not reach puberty?
Second, the source of theology in islam is primarily two. Its not only Quran but its also sunnah (the teachings of the prophet (saw) ). This is the fundamental principle you need to be aware of.
Third, it is not these issues that define a prophet to be prophet. Its a comprehensive objective look at the biography of this man that led to many believe and put faith in him that he was indeed a prophet of God.
Fourth, its wrong to project contemporary standards in these civic matters to a society that was 1400 years. There was nothing wrong to have such a marriage in that society when a girl has reached puberty.
