If Khomeini had remained in Iraq, he most likely would have been killed by Saddam Hussein in his rise to power. Note it was Saddam when he was VP of Iraq who told Khomeini it would be better for him to leave, and then both men once they rose to power would bring the 8 year war. Given the chance to consolidate his power Saddam would have killed Khomeini, he would of been a threat to Saddam's desires. It is very likely the official story would be that Khomeini had died of natural causes due to illness.
With Khomeini's death I'm not sure the Islamic faction would have remained as organized as it did, as such I do not believe it would have been capable of throwing out the Shah of Iran or ending Persian rule. It does not mean that it would be an easy rule, there were many groups opposed to the Shah, just none of them particularly organized.
Reza Pahlavi would become the new Shah of Iran in 1980 when his father dies. He would continue western reforms which largely anger the former Khomeini followers, the problem is they lack anyone to effectively take Khomeini's place yet. If he is able to get inflation under control and improve the average citizen before the mid 80s I think he could avert the revolution for his reign. Otherwise if he can't do that then its going to happen you just need a new leader to rise and gain power, that would probably take 10-15 years, so you'd be looking at a Revolution in the early to mid 90s, by then though there could be stronger voices from the other opposition groups, who mostly sought for the Shah to conform to the constitutional powers so while a revolution and the fall of the monarchy could happen still by the mid 90s it is not necessarily an Islamic one.