I was on the same cruise--Majesty of the Seas, 3 nights--last fall and really enjoyed it. I'm afraid I can't recommend it, though, for singles, as everybody seemed to be "coupled." The singles party was a bust, because no one from the ship was there to make intros and get things going. You will have a good time, as I did, because it's a nice ship, good entertainment, etc. Plus you are going with your own group. ( Read my review <Cruisemates.com> )
As for the island day, it was wonderful! But take your own bottled water, beach shoes, and suntan lotion. Towels are provided.
Have fun and let us know here on the message boards how it went when you return.