What am I missing, or indeed missing out on?
hahahaha.
In a more general sense, I would go to Pakistan with an open mind. Rid yourself of the notion that Pakistanis hate Americans. People in Pakistan are appalled by the conduct of the US Government in their country (and what level-headed individual isn't?), but it does not mean that they hate the citizens of America. Being a Muslim may well impress her family, especially if you live up to the ideals of the faith, but you are still absolutely a foreigner and outsider to their culture. Her father is not going to shoot you for being interested in her, but you need to work out your pitch, preferably after getting to know the family face-to-face.
If you have never been outside the US, or outside western countries, you are in for a shock when you reach Pakistan, though Islamabad is actually fairly westernised, on the surface at least. Try not to measure everything up to standards in the US, and remember they live in a culture which is far, far older than that of the US.