I didn't even know about Hobbit Day... however, reading the article here about it, it probably should have been yesterday, since The Hobbit was published on September 21, 1937. It seems that September 22 is based on a misreading of the Shire calendar as the same as ours.
Which is not September 12... but could be depending on how you think Shire calendar translates to the Gregorian calendar. Seems like celebrating it on the day we are certain that The Hobbit was published is better.