I think in the case of Islam those issues aroused as soon as Muhammad died. Since they had nothing resembling a quorum of the 12, they first schism (split in two factions) happened right on that spot. We are not sure when the Qur'an was finally assembled but it seems about 20 years or so after Muhammad's death from written sources or memory. Just like in any other religion without ecclesiastic structure, different Mullah Iman (leaders) instituted its own worship rites and traditions which in time became dogma rather than doctrine. In fact, much of Islam today has nothing to do with the Qur'an and a lot to do with tradition. Much like Rabbinic Judaism which augmented the Law of Moses to thousands of commandments.