It is curious why the OP asks the question how to pronounce Doge. Perhaps he knows the real origin of the word which came from Venice.
The Doge of Venice was a political and a judicial head of the city. The Doge became, according to the Whig interpretation of history, a symbol of foreign and almost oriental type despot, hence the Doge of Venice was for them the embodiment of absolute and therefore arbitrary power.
Doge, pronounced as dohjj, or if its easier for you, a bit like doze but pronounced dozhe.
Hope that helps.