Islam is fairly diverse. The rules for conduct in Islam cannot be broken down into black and white anymore than one would with Christians or Jews. Catholics and Lutherans do not hold the exact same tenets, nor do reform Judaism and the Hasids.
And you can break that down even further in all instances.
People have this tendency to be more nuanced than the sum of their group's parts would lead you to believe. Talk to her about her faith and tenets. Get to know her faith (and it's actually a great way to get to know someone better as well).
FFP2 said:
Don't even attempt to do anything intimate with her, they tend to not do things the same way non-muslim people do (not insulting, that's why I love Muslim people)
Oh, and don't bank on getting serious unless you want to convert.
I know a few Muslims who would be quite angry and/or upset about this. And considering I've heard this sort of thing about Native North americans (I'm half Penobscot), I can totally understand why. That's sorta...Bigoted, intents aside.