Depends on your girlfriend and how close she is to her parents. My DH asks for my parents' blessing, and though my sister is as independent as it gets and no one's opinion is going to stop her from marrying the man she wants, she knows it would be important to my dad so she's told her boyfriend to talk to my dad first.
You're in a slightly different situation since it's a big surprise for her, right? Any way you can mention the idea to her and see how she reacts?