Why would it be looked down on? Are you a 68 year old guy and she's a 19 year old? Aside from a very large age discrepancy, I don't see any reason it would be looked down on.
You won't know if you don't try. If you ask her out she might say yes and you get a date or she might turn you down and you don't get a date. If you don't ask her out you don't get a date.
(DISCLAIMER: This message typed by a guy who has never even gone on a date before, so I could be wrong.)