Sorry in advance, I know it will be a long post, but I wanted as much info as possible before we sailed so I'll try to help as much as possible.
Scrappermcl, cruising with our daughter was great-much easier than staying home for me! Part of that is due to not having to cook, make beds, etc., and the rest because my daughter prefers to be held most of the time and since you're constantly moving from place to place on vacation she was carried in the Baby Bjorn so she was a very happy little girl.
Definitely take a stroller as my daughter slept in hers at the table during dinner, which worked out well since at 3.5 months she was definitely not sitting up yet. Now at 4.5 months we might be able to get away with a highchair for a little while, but I would still want the stroller. Also, the Baby Bjorn was invaluable for carrying her around the ship when you don't want to take the elevators (which you had to with the stroller) or to the beach. The elevators are very tiny and slow so we often had to wait for another one when another stroller family was already in the elevator. I mention the stroller as we almost didin't take ours since a friend who cruised with a baby told us it was too much of a hassle to lug around the ship. This is not true, and if you use Flounder's you can bring it in there too.
About Flounder's Reef. I had mixed experiences with it. We were in a suite and the concierge let us sign up for every night of the cruise when we boarded instead of just the 3 nights that Flounder's tells you, so we decided to sign up every night so that we could bring her for a little while each night to get used to it so that when we had dinner at Palo she wouldn't be in shock at being left (she's never been away from me besides one night with grandma). Well we dropped her off the first night for about half an hour (there's a 2 hour minimum but we didn't want her there the whole 2 hours). We brought her Ocean Wonders travel swing (another blessing to have with us) so she'd have something familiar and put her in that when we left. There was only one other baby there and 3 CMs so we felt good about leaving her. When we got back she was in a rocking chair with a CM almost asleep and she actually cried when I took her back! So I figured she liked it and liked the CM watching her so we were happy. The only thing I didn't like was that they said that if the baby goes to sleep, they put them in a crib in a separate room in the back and only check on them every 20 minutes. There are doors up and when other kids are in teh main room it's loud enough that you wouldn't necessarily hear a crying baby in the back. Anyway, the next night we went to drop her off but the place was mobbed with kids, most of them crying. They were way understaffed and each CM was holding at least one child and pushing others in a stroller with their foot. So we took her to dinner where she slept in her stroller happily. They didn't charge us for that night because they were obviously overbooked and were probably happy we didn't stay. We cancelled the other booking, except for the night we went to Palo and we changed that reservation and Flounder's time to 6pm (when Flounder's first opens) so that it would be less crowded. When we dropped her off we put her in her travel swing and told them to page us right away if she started crying, which they said they would. We never got a page so we finished dinner and came down to get her about 90 minutes after we dropped her off and she was in another back room (not the crib room) in her swing and she had obviously cried herself to sleep. They told me she had just fallen asleep and they didn't want to move her so they let me in to get her and she was in her swing doing the 'sniffle breathing' that babies do when they've been crying for a very long time. Obviously I was very annoyed since she was only 3 months old and who wants to know that their daughter was that upset--my dinner is not that important to me which is why I specifically said to page me if she cried! I should have said something to them, btu since it was our last night on the cruise and I knew she wasn't going back there anymore I just took her and left. If you have a 2 year old, I'm sure they'd enjoy Flounder's and the low # of CMs wouldn't be such an issue, but infants are a different story.
Most shore excursions allow babies, but we didn't want to do many of them with her. We did the Blue Lagoon beach day, which was a beautiful island. It was school field trip day though so it was very crowded with local middle schoolers, kind of like a town pool or waterpark, but the kids were all very nice. Something like the dolphin encounter is doable since you take turns in the water, but we thought it would be too hard. We could have done the glass bottom boats, but my husband gets ill on those tiny, rocking boats. But the beach day worked well and at
Castaway Cay we stayed on the beach too. My advice there would be to get there very early to get an umbrella moderately close to the tram stop. We got there at 10am and we had to walk to literally the last row of chairs to get an umbrella, which is a necessity with an infant. Our dr said sunscreen was okay for her to use, but they don't all feel that way so check with yours before you go.
Other than the one bad night at Flounder's, we had a great cruise. By the way, almost everyone in our dining rotation ate at their own tables, unlike other cruises we've been on where we've always sat with other guests. Either way is fine with me, but I know some people are concerned about their baby bothering others at dinner (though really if kids bother you it's the wrong cruise line). The pictures we have of her on the beach and witht eh characters are invaluable. Any more questions feel free to ask me. Congrats on the baby and have a great cruise!