I have a water baby, we actually had rangers come out and "assist" us because they heard her screaming at 18 months old while kayaking. The rangers had a laugh when the saw what was happening, she was in her life jacket, swift water throw rope attached to me in slow moving flat water. She climbed out of the kayak and was swimming along side as I paddled very slowly, the screaming was every time I tried to remove her from the water to bring her back into the kayak.
I can see from your post you and your wife has a passion and now a new little one! I share the above story to show that your little one can and will share in your adventures. I do feel that 6 months old is too young to be on a snorkel boat and I would not leave a child that young on board the ship without an adult.
If you do decide to leave little one on board please only book a ship excursion. If you book private in that situation the ship has no way to reach you should something happen to your little one.
I would recommend if you want to bring little one consider also bringing grandma or grandpa to watch little one.
What is your purpose/goals for this cruise? A family time experience, deep sea snorkel and dive trip, combination of both? Only you can make a decision for your family. My daughter is almost three and is ready for her own kayak, still attached to mom but with her own paddle and boat. She has her own life vest and has been in swimming lessons and pools at least three times a week. At 21 months she took her first cruise, she wore her life jacket and swam with me to see the fish, she had a snorkel mask but no snorkel. Instead she put her head in the water and blew bubbles or held her breath. At 3 years old on our January cruise she will have her mask and a snorkel.
You will get there as a family to enjoy these experiences but it is a gradual and often slow process. You as the parent can only go/do as much as the little one is capable of at a given point in time.
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9/2012 - Norwegian Sky - Bahamas - 4 day (OS - SB 8001)
1/2014 - Norwegian Dawn - Western Caribbean - 7 day (DOS - SA 12500)
3/2014 - Norwegian Breakaway - Florida and Bahamas - 7 day (B2 - 12168)
2/2015 - Norwegian Dawn - Western Caribbean - 7 day (SJ - 12018)
3/2016 - Norwegian Getaway - Western Caribbean - 7 days (B2 - 12238)
Dreaming of a European Cruise - Baltic Capitol