It's absolutely fine all year 'round. You have to watch for hurricanes closely during the season, but there's usually plenty of time to avoid them.
Temperatures only vary by 5 degrees F
winter to summer. Winds are a bit lighter in the summer and tend more from the E and ESE, while in
winter they take a more northerly slant from the E and ENE, with the occasional norther (the so-called "Christmas Winds").
Bottom line: September is fine.
Bill