I believe I did a short cruise on the Fascination -- could have been a sister ship, maybe the Fantasy? I went out of Jacksonville . Tiny rooms, older ship? I think it had a nice water slide. The shows were like musical reviews and not the best for kids.
Generally, Carnival ships are colorful to the point of garishness . The Wonder is a classic style ship with beautiful, classy art nouveau designed and amazing attention to details. Your room, unless you had a suite on Carnival, will be much bigger. There will be a bathtub in your room. One thing that may be the same on both is that the kids pool(the Mickey pool) will probably be very busy. But unlike Carnival, there are lots of other things to do with a small child.
All shows in the Walt Disney theater at night are family friendly, and the big production shows, which you will have 1-3 of depending on the length of you cruise, are actual shows, with a plot etc. I love them, and love going with my kids to them.
There are family friendly activities scheduled all day, and with Disney they CATER to little ones, you won't feel out of place with a child in tow, except:adult only pool and cove cafe, where kids aren't allowed, and the bars, of course, and late night adult only shows. Of course, "adult only" on
DCL is the equivalent of PG13 in the rest of the world.
With Carnival, I feel like the "heart" of the ship is the casino and you can't go anywhere without passing by it (which I hate). On the Wonder, there is no casino, and the "heart" it is the lobby atrium, which is often filled with character greets, baby races, golf competitions, etc.
Your daughter is too young for the kids clubs, but DEFINITELY take her to the open houses (there is an hour or two every day) as there is lots you can do with her. I don't know if the nursery has open house hours, but if they do check it out... You might even decide to use it for an hour or two!
Check the navigators every night as a lot of activities for younger kids are earlier in the morning... Like a Disney Junior event I think is held every morning. Your two year old may get a little ansie at dinner as they run a little long. At that age you will probably want to do some character meets, and if she likes Anna and Elsa get tix as soon as you get on board for her to meet them, and get "warm hugs" from Olaf.
Oh, and the movie theater shows movies all day, and there are lots of kid friendly shows on tv.