We sailed on the fantasy last January (2015) and we went to Trunk Bay on our own. DH and I have been to St. John numerous times so we are comfortable with the ferry situation. But it's entirely doable as first timers. What exactly do you want to do on St. John?
The best way to get there is to grab a cab at port, take it to Red Hook. Take the ferry over to Cruz Bay and cab it to wherever you want to go on St. John. Be mindful of your all aboard time and the ferry schedule. I would make sure to leave St. John at least 2 hours before the all aboard time. The ferry ride between islands is roughly 20min but sometimes the cab ride between Red Hook and the port can take awhile, depending on traffic.