Aisha: Thank you! :-) If I decide to convert, I don't want your father to have doubts when I will ask for your hand!

Dvargas: that's the point. There is no procedure of "conversion". According to Koran we all are muslims, but we have to accept it. There is no rite to follow and there is no authority to execute a conversion rite, like in Roman Catholic or Orthodox church.

The closest I suspect might be a witnessed declaration in Sharia court by somebody who knows you. But it would be interesting to know what your landlord will say.