Don't treat her like an alien... it's possible that she would go out with you, but the physical sides obviously not going to be much. The 'Hijab' headscarf is taken off at home, but she probably wouldn't take it off in front of a guy until they were at least engaged...
It depends what her atttude is, some Muslim women are very careful about ''going out'' because in their culture that means that it's a fairly long term comitment (i.e. if you 'went out' properly she might expect you to marry her) but other girls aren't like that. Of course you can't go clubbing or to the pub... but you can do things together.
I would guess, tell her that you'd like to get to know her better (don't mention 'boyfriend' or 'going out' as such), and ask her if she'd like to go to the theatre or cinema with you, or talk in a coffee shop or something. Probably best not to try and make any physical contact... once you get to know her better you might be able to work out where she stands on dating.