The only way your going to get alone time is to take a sitter with you. You can just chalk this up to a family vacation where you get to spend a great cruise with all of you together.
I suggest you take a baby pool so you can sit by the pool and the baby can splash. There are several excursions you can all go on together.
Just remember to pack everything your baby needs. There are limited supplies on board and I don't remember seeing any baby food.
Life is too short to let the ship of your dreams sail without you.
Carnival Destiny Feb. 2006
Carnival Fascination Feb. 2007
Royal Caribbean Grandeur of the Seas Feb. 2008 The DTW & MsBJ tour
Carnival Valor MsBJ and Dina Feb. 2009
Carnival Glory MsBJ and Dina Feb. 2010
Carnival Dream MsBJ and Dina Feb. 2011