Hi. Since you are new to cruising ( and obvioulsy new to travelling with a child) may I suggest you don't bother with a ships " excurision " at all. They usaully entail waiting around in lines, getting in and riding around in buses, and of course shopping. None of these things rate high with babies. An exception might be a tour that goes to a zoo, kids( even babies love animals).
We took our then 6 month old and 2 yr old on a cruise and just grabbed taxis to nice beaches. Rent a big umbrella( or bring your own) for shade, take a few sand toys, and let the little one just enjoy a beach day.
Obviously take lots of sunscreen ( and put it on BEFORE going to beach), and a water bottle, and have a nice relaxing day off the ship.
Depending on which ports you are going to( you didn't say) some are hard to get a stroller around( uneven pavelment and potholes everywhere) and so shopping isn't that fun. What you could do( we did) is do the beach day part first, then before returning to ship you and hubby split off, you to shop for an hour ( the shopping aresa are usalully near the ship) sans kidlet and he proceeds to ship. You could take turns doing this if hubby is a shopper( are there such things?) and then hubby could take child in for a wash( salt water, yuck) and a nap. Hope you have a handy husband that way, it will make the cruise way funner for all of you if he is a good load sharer.
Have fun, and may be post which exact ports you are going to so you can get specific info .