No, we AREN'T! We are a Constitutional Republic.
Simply ask yourself this...what establishes the representation of which you speak?
As you have things, you're putting the cart before the horse.
America's government is officially a constitutional federal republic.
However, the more important aspect of constituting America is Article 4, section 4 of the Constitution.
The United States shall guarantee to every State in this Union a
Republican Form of Government,
and shall protect each of them against Invasion; and against domestic Violence.
Thanks for the correction. All else is true.