With most coastal cruisers (and I haven't looked up the lines or the numbers on this particular vessel type), the problem isn't "is it strong enough to do the trip?" but rather has to do with the motion of a lighter-displacement boat designed to keep going in light airs when it hits steady 25-35 knot winds and long rollers of eight to 12 feet.
If it's a spade rudder fin keeler, it might not heave to well at all, and while it might move smartly under the right sail set (and who's steering actively when you are taking in a reef?), it will probably want active helming to avoid broaching or going wildly off course, particularly if you are sailing close-hauled and need a bit more foresail to punch through waves.
Portlights and hatches may be an issue. The stock deadlights of many production boats WILL leak or even give out when hit the wrong way by a ton of water. The hull might survive, but if you are pooped and your plywood 1/4" companionway drop boards shatter and let a ton of water below, you and your boat might suffer the death of a thousand splashes, so to speak. And again, who bails while you steer, check for chafe, adjust lines and keep a watch?
Lastly, there are certain calculation that can give an idea of how "whippy" a boat might be at sea. Some boats and skippers do fine, even with the caveats listed above, only to fall prey to persistent sea-sickness due to the rough, "snap-rolls" some fin keelers can produce. Either that or they can get injured when a boat falls off a wave or rolls 50 degrees and they break an arm.
All this is definitely worst-case scenario, but the trip you are proposing (counter the usual Gulf Stream current and with a shoal-surrounded destination) is among the more challenging you could tackle, certainly as a first solo trip.
I would recommend trying to do deliveries on similarly sized fin keelers. Now is the perfect time of the year, as many cruisers in the Caribbean are heading north soon. At least if you are in a crew of four, you can take a break and know you've got backup of a presumed but likely level of competence.