I cruised solo from Genoa to Fort Lauderdale on the Costa Atlantica in 2002. It was wonderful! The Italian flair of the ship and passengers made it even more special - more like a real "ocean liner crossing" than a regular cruise (not that I mind those at all!).
I'd do it again in a heartbeat. The extra days at sea are wonderful for meeting people, reflecting, relaxing and just enjoying life!
Just do it!