M.W.
Try a Royal Caribbean cruise to the Bahamas. We LOVED it! Our daughter was 9 months old when we did this one and we had a great time. Great food, great entertainment, and great sites!
We also did a Carnival to Mexico and it was a total "party ship". We didn't care for it AT ALL! And our daughter was 3 1/2 at the time and HATED Camp Carnival. Our son was 6 months for this cruise.
One suggestion. Don't book any excursions ahead of time. We found that out after our first cruise. It's much cheaper to WAIT till you get to the stop and then book things OFF the boat! That way, you're not paying the cruise ship for their "share" in the sale.
Your daughter will have a blast with you! Our kids were NEVER bored on the cruises and neither were we!