Dear friends, as I see it the idea of rule of islam is very very far away. Why?
Because before we can do so we need to understand the quran properly and interpret it correctly. We also need to sort out problem with ahadith collections ie we need to sort out genuine ahadith from the made up ones. Then we need to interpret them properly too.
After that we need to convince people at large about these and then leave it to them to bring about the rule of Allah.
Rule of Allah will come in its own time in its own way as predicted in the quran very clearly regardless of muslims and nonmuslims.
When people have enough education to see islam for what it is that will be time that all will be happy with it.
Islam is not about structures of governing bodies but a system based on some fundamental principles. So long as those principles are basis of a serving system, it is islamic.
If anyone has read Surah Yusuf 12, he will see that king of egypt had his own religion yet prophet joseph was happy to serve the kingdom of egypt under him and even brought his father and brothers there. He turned egypt into a just kingdom the religion of ruler was of no significance.
The quran is also clear that your parents and relativs can be of any religion, please surah 60. So long as they accept same moral right and wrong in term of humanity, there is no problem as far as islam is concerned.
Islam is all about fight against oppression, suppression, aggression, hate, cruelty etc ec.
The law in islam is not shariah as it is in books written under cruel muslim rulers. They got them written to secure their own rule not islam. They destroyed the proper understanding of islam and that is why we are suffering even today thecurse of sectism.
They got it destroyed because it stood in their way of ruling.
The proper shariah laws are very different from what has been taught by our mullahs from books of fiqh.
This is why this is the very first thing we need to do ie discover the genuine islam from the quran and the hadith. Only then we can talk about structure of government.
regards and all the best.