Hey mate I might be able to give you a better opinion than some here - as my parents are very strict muslims where im not.
Muslims girls are really under the thumb under the parents, if you told her you like her and she feels the same and you do something you will cause her unbelieveable amount of trouble - you wil bring massive shame upon her and her family, so much soo i'd imagine they'd kick her out she'll lose all the close relationships she has with her family and a lot of her friends too, you will quite frankly change her life. Or the family might force her into an arranged marriage or take her abroad then you will definately lose her forever.
Only the flipside, like I expect, yeah she probably does like you, but even if you asked her she won't go for you as muslim girls are very very family orientated and they would never give that up for a guy.
Basically how much do you care for her? Don't mean to sound 'gay' but do you care enough for her to leave her alone? As you getting with her might cause her more trouble than it's worth especially if it didn't work out.
What i'd do? Try and make her more independant, let her decide herself whether she wants to live a westernised life or not, once she breaks ties with her family (she eventually will have to when she is asked to get an arranged marriage or not) or stays with them make your move, if she desserts the family go for it, if not leave her be.
EDIT: Ignore what I just said, if she's half egyptian/greek/turkish or whatever parents aren't anywhere near as bad HAHA and they're not into arranged marriages? Go for it mate seriously.