If you're going to do it "just for fun" and rush into it. You will not have any fun. It'll actually probably be awkward as neither of you know what the Hell you're doing. No one here can tell you what you can and cannot do, though. If you guys end up having sex, then you guys end up having sex. It's that simple. But I guarantee you'll regret it. Or feel even worse about yourself than you do now.
Expect her to ignore you, expect her to tell her girlfriends you came in 30 seconds, expect to feel like crap, and expect it to awkward. Not saying all of this will happen. Just giving you a heads up.