I would never convert to Islam because I don't care for the dogma. I also don't like how predominantly Muslim regions tend to have some rather harsh laws & customs relating to religion & spiritual practice (e.g. en.wikipedia.org/wiki/Blasphemy_law_in_Indonesia ). That's to say nothing of what happens when you're Muslim and decide you want to go a different route...
Also, I would strongly advise you to not marry a girl you're never even kissed, much less slept with. A significant component of a healthy, vital relationship is a good sex life, and some people are just fundamentally incompatible sexually, even if they are perfectly compatible in many other ways. You won't know until you've been together, and it just seems like a big risk to take.
This situation seems to have a lot of red flags in general, though. Five months of conversation to the emotional depth of love, and she's just now telling you that marrying a Muslim is important to her? Entirely LDR thus far, yes?
Maybe she's "The One" for you (validity of the concept notwithstanding), maybe she isn't. However, I believe one thing rather strongly: Any girl who wants me to "compromise" by giving up things truly and deeply resonant with me is certainly not right for me. She should support me in those things, even if they are not also her things.