It's only your ego worrying about whether others will scoff and shame you for dating someone half your age. IGNORE IT!
Look, we live in an age where gays are pushing for the right to marry, but people still cast stones at someone who wants to date another grown, legal adult of the opposite sex, just because she's of a younger age. Of course, these same people see no problem with cougars picking up little Ashton Kutchers.
This "societal norm" is misinformed, and based on the following: 1. May-December relationships are unusual. 2. Older females resent having a guy their age "taken" by a younger babe. 3. Average, frustrated men of all ages resent a guy who can date anyone he pleases. People also will tell you that you're "supposed" to be settling down already. Ignore, ignore, ignore.
Have fun with it and keep in mind that she's young (read: probably immature).