Problem

I`m a 27 yr old Muslim. A while back i met this girl from school she approached me and started asking questions about Islam its been almost 2 yrs as, time went on we found we had a lot in common ( we did not date ). She wants to become a Muslim and has done extensive research on her own. She did a lot of stuff which were bad, but i think it was because of the fact of where she was and the company she had with her ( she used to sell drugs and other stuff is which is not permitted in Islam). She is completely different now and regrets what she did in the past to a point where she cry's almost every time she talks about it.

I want to get married to this girl because she`s a good person and i know she will be a good Muslim too, my problem lies with my parents they are very old school and always mention how they want me to get married to a good Muslim girl. Most of my cousins have actually married out of Islam and their wife's converted into Islam and my parents say they have no problem with it but think they got into Islam because they wanted to get married ( being a Muslim by name basically ) I do not know how to approach them and tell them that i want to get married to this girl.

She is a christian right now and her parents are too.