I don't think so, but then maybe I'm old fashioned. This phrase is used very naturally in many contexts, such as football, business, and social situations. Managers sometimes use if it in press conferences after an important win, and this headline from 21/06/2013shows it is pretty common - 'Luna over the moon after sealing Villa move'

Other phrases could be: really pleased (more formal - and a bit boring), psyched (modern, casual), chuffed (very British)

Yes I agree that it is still a fairly common expression but the headline is also a pun as the player's name (Luna) means 'moon' in Spanish.