Actually i was also facing the same problem as you are facing now and for that reason i had posted the same question here but none answered it....

You will mostly find the Islamic History books starting with the topic pre-Islamic age and mentioning the contents regarding Arabia only, but the question sometimes comes or may be asked comprehensively regarding the world before Islam which does not mean you have to write down Arabian scenario only. I am going to write down few points which may be helpful for you and study them in detail.

The world before Islam starts actually from the Semites(Semitic races which then developed into Judaism, Islam and Christianity) The chain of the world before Islam is starting from the Semites, Assyrians, Phoenicians, Akkadians, Babylonians, Arabia, Mesopotamia and Persia. You have to briefly describe these major civilizations and it will cover the topic the major civilizations before Islam or the world before Islam.
I will happily answer your query if you have any other regarding this or any other.