I have cruise and followed a hurricane (last year). IF there is a storm in your cruise area, the cruise ship will change course and/or ports to steer WAY clear. For the Liberty, it does alternate Eastern/Western Caribbean cruises.. so if there is a hurricane in the western cruise locations, they might change the cruise to the eastern. Or like in my case, they just reversed the ports of call order so that we "followed" the hurricane instead of getting in its way.
The biggest concern is if the hurricane hits your embarkation port (in this case Miami) when you are supposed to be boarding. Either the ship won't be able to get into port on time OR it may need to leave early. More likely your flights into Miami will be affected (if you plan on flying in the day before and staying overnight, that mimimizes that risk.
IF you are truly worried about it (Except for my Alaskan cruise ALL of my cruises have been in season and I have not had a cruise cancelled yet) take out trip insurance to cover the possibility that you cruise is affected. IF you have a choice book it as late into October as you can, the season officially ends n Novemeber but the later you can push it that less chance of a storm
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013