I remember when I was in 6th grade we did a genetics wheel and identified dominant and recessive genes with a number of different traits. I think I had a freakishly large amount of recessive traits listed. Blue eyes, left handed, I could do the tongue roll thing, and I could completely flip my tongue. I think the only dominant I had was my sandy brown hair. So, I'm a mutant is I guess what I'm saying...
As for the original question, I believe that genes that lead to the stereotypical concept of "Asian" appearance (eye color, eye folds, straight black hair) tend to be dominant, so they would be likely to show in children. That said, though, I'm sure your appearance is fine. You've got to be happy with your own appearance as it doesn't define you as a person. It's just window dressing. Your girlfriend is obviously happy with how you look, if you're talking about having kids, so that counts for something. Besides, having kids isn't about which parent they look like, or even what they look like at all. You're talking about caring for someone enough that you and they want to bring another human being into existence to share your life and your love. That kind of transcends genetics and appearance. It's about opening your life to someone new and leading them forward, guiding them through the world, watching them grow and have experiences of their own. Whether they look like you or your girlfriend, the love and the journey is what is ultimately important.