I wish you had indicated how old you were, because if you are of an age where this could develop into a long term arrangement, that is different (to me) than simply dating. My advice assumes you are old enough to make long term commitments.

I think you should NOT underestimate the religious differences. Even the most liberal and tolerant of people experience difficulties in this area, because even though young romantics don't like to see it, unless a couple is willing to abandon their families, they WILL have an impact. Religion may not make a difference in the beginning, but it becomes very important during life cycle events (especially birth of babies) and even holiday celebrations. Family traditions pull at you in a deeper way than you can imagine.

That being said, I think these things CAN work out. One of my closest friends is a Catholic married to a very lovely Muslim man (yes, their families made them miserable about it, so they moved here to America). I, too, married someone who was not of my religion, but I eventually abandoned my family's religion altogether so as to have unity in my household. I'd suggest before you date this girl seriously, you both ought to learn a LOT about each other's religions so you can see what you are getting in to.