Same day? I'd be nervous. You have to go through C&I at the ferry wharf and at the airport. The STT airport recommends being at the airport three hours before your flight. Optimistically, you'll be at the airport at 11:15. Pessimistically? Next day. Good news, you're on Speedy's ferry.
In order to have the best possible chance, go carryon only, preprint your board pass and have your immigration forms pre-filled.
http://www.cbp.gov/sites/default/files/documents/CBP%20Form%206059B%20English%20%28Fillable%29_0.pdfYou'll need a plan B unless things go perfectly for you. We've done same day rebooking to a later flight when we've hit a travel delay. Have your airline on speed dial and your confirmation number handy. Barring that, Best Western Emerald Beach has a nice beach and is near the airport.
Cheers, RickG
