karthik, I suggest you wait a while. Your chart has a very early degree rising, which generally means that it is too soon to give a correct answer to your question. Circumstances may change, for example.
The significators in this chart-- you, your girlfriend, the parents-- are all Mercury and Jupiter. Jupiter (your GF) is in the 12th house, which suggests that she is not in a strong position to help your case. Mercury is just past a square with Jupiter, but it is going to conjunct Saturn, which usually is not a good indicator. However, the moon is going to trine Jupiter, so I do not think your situation is hopeless!
Rather, I think it is just a bit too early. See if you can find out more about the parents' objections, and how you could better counter them, for example.