Depends on the parents. If she is worried about telling it to her folks you are sure to face some trouble. In India we do have lot of inter religion marriages. But only when the parents are open to it.
In the worst case her parents might disown her. And might never talk to her again. See how things goes after confronting them and do what is best for her if, you love her.
Can elaborate on what kind of Muslim" and if she is from another country, like Egypt? Pakistan? This would give me a better understanding of your situation. Where are you from? Need some background, cause its entirely different circumstances. I went out with a Pakistani guy when I was in college. I am a caucasian female. I studied Islam, we were actually together for 3 years. He was educated in a British boarding school, his father worked for Aramco, in Dharan Saudia Arabia. When his parents found out he was dating me, he had to go back home! They are a very strict religion & culture, there are many dynamics involved. He was arranged to be married before I met him! So, your entering into a complicated situation
Her parents cannot approve of this in Islam as the male head of family must also be Muslim. Have you thought of converting to this fastest growing religion in the world? It would be a huge responsibility to marry someone who can no longer participate in her own family. Even if she later realized she misses them and thinks a divorce is a way to get them back, a Muslim family would still not find her acceptable and she would never be solicited by her family to a Muslim male as they have arranged marriages. She would likely never be able to marry again except to a non Muslim if she chooses to defy her family again. Please read about this religion so you understand what harm you would be causing by this marriage if you do not convert to Islam, and to also see if this is a religion you could embrace yourself. my husband is Muslim we have been together for 17 years. I have not converted, but I know the religion well.
Depends on how dependent (or independent) your girlfriend is. If she is independent, what her parents think about the situation will not make a difference. Some women are very tied to their family and breaking that tie is emotionally difficult, maybe even impossible. You both need to speak as ADULTS. If her parents object, will she give in to her parents wishes or will she challenge them? If her parents disown her, will she be OK with that? If her parents refuse to see her (or you or your kids) will she be OK with that?
These are permanent non-negotiable decisions. She has to realize that she can't change her mind later. The reason is that the family has emotional power on their side. They have each other and she won't have anyone (except you). If she changes her mind, that gives the family more power and it degrades her position. When you are emotionally vulnerable, that is NOT the time to think about these questions - you will be taken advantage of. You need to answer them NOW - definitively and absolutely.