i'm asian, and i know for certain that my parents would definately be against me forming a relationship with someone other than of my own race and religion. Hell....they'd be definately against me forming a relationship full stop, with the business of arranged marriages and all that (which i am NOT opting for btw), but thats a whole different kettle of fish.
i'd say it is possible to carry on with your relationship, but be prepared for some friction when everything is out in the open. Yes...her parents (and possibly even yours) probably will try and break you up, then again they could be cool with things and let you carry on as you are. You wont know until you tell them. Oh yeh, and another thing, i know both you and your girlfriend are adults and everything, but indian families prefer the boy to be older than the girl (going with tradition and that), so it doesnt help that you're younger than her.
Having said all of that, i know some people who were in your situation, and everythings turned out well for them. An example of this would be of two teachers at my school. The guy's white (teaches maths), and the women is like in your case is indian hindu (teaches science). I know them both quite well, and by what ive gathered, things werent too rocky for them. Well about 2 years ago, they got married, and just recently they had a baby, so all is well.
I hope everything goes alright for you and your girlfriend
Good luck!
(p.s. keep us posted on the latest wont you!)