It depends on how religious she is and to a lesser extent what her family is like. Technically you aren't supposed to convert to be with a Muslim woman but again, it depends on her own view on this.
I know way too much about Islam and I would say if neither of you are that serious about the religion it could work, but if she is serious about it (like wearing hijab or head covering of some kind all the time) and you aren't, don't bother. It's a religion based on an almost neurotic fear of God and the "hereafter," but of course a moderately religious person would view this more subjectively. There are way too many rules to follow (for example, you aren't supposed to listen to music and there are even rules about how you are supposed to clean yourself after going to the bathroom) and if you don't care and she does, it will lead to a lot of problems especially if/when you have children.
You should talk to her about it more if you are serious about this girl. Chances are she will be upfront about what she expects of you and you will get a feel for how she interprets the religion before you invest too much time into her.