Well, based on your age I'd say that you should ask yourself the same questions you posed. Are you looking for a woman to have and to hold, to love and to cherish, to raise a family and work out a bidget with? Are you just wanting to get to know her better for non-romantic reasons or do you want to see what becomes of the date? Answer yourself honestly: What do you want to see happen during the date?
I met a girl who was not Christian, had sex with her like I had so many others, conceived with her and married her. The first six or so years of marriage were tough and we both became very apathetic toward God and church, rather than fight about it. And we did fight quite often about money, jealousy, parental responsibilities and much more. Each of us thought we were in the right and there was no mediator, such as we have in the Bible.
I have (obviously) come out of that, and my wife is a "baby Christian" as well. The Lord has been faithful to restore our love for each other, but it has not been easy. Likewise, we are at different spiritual ages, so to speak. I love to read from the Bible and she prefers to hear it from the pastor at church. This doesn't sound so bad to some, but it really can complicate things. Consider this commandment from the book of Law:
Deuteronomy 22:10
You shall not plow with an ox and a donkey together.
Does this mean nothing to someone who isn't farming or who has a tractor? Was the purpose of this verse good for a time, but irrelevant today? I encourage you to think on this as you consider who to seek for romantic dating purposes. Marriage is work, and when the partners aren't able to work together problems can result. For your own sake, I suggest courting Christian girls. By all means, you should be friends with others, but not for romantic purposes.
You may want to date a girl who you don't know to be Christian or not, and I don't see a problem with that. But I would find out where she stands before you get any more serious than a date. Until you find out, keep things at the friend level. I didn't do this and truly wish I had. I love my wife dearly and thank God for her, but that doesn't mean I took the best route in finding my wife.
Hope this helps!