Actually, the Dodgers WERE in LA in 1962, the year the movie takes place...they played their first game there in 1958. So it was possible for Benny to have the hat.
I agree with the other person who said basically teh same thing, the Dodgers were already in L.A by the '60's. They first moved to Los Angeles in 1958 and played their first game in Dodgers Stadium in 1962