Megan,
Our family's first Disney cruise was also the 4-day. My daughter was 6 at the time, my nephew was 4. They both enjoyed the Oceaneer's Club. Unless your child is inseparable from you, I don't think it should be a problem to have him or her in the Club. The councellors are very attentive and there are a lot of them. They plan lots of activities and they do a good job of keeping them engaged. You can even put the kids in the Club while you are at Castaway Cay if you'd like to go to the adults-only beach.
Things not to miss? Tough to say b/c on the 4-day cruise, there's so little time. You definitely want to hit each of the main restaurants. If you can make a Palo reservation online, that's great, but you don't want to miss one of Triton's, Parrot Cay, or Animator's Palate.
I don't know if the show "Golden Mickeys" runs on the Wonder or not, but it's my favorite of the shows. "Twice Charmed" is the new show and I haven't seen it yet, but you should probably not miss it.
I really enjoyed the Navigator Series tours, and my wife loved the culinary demonstrations. My daughter loves Scoops (the ice cream station :animwink: ).
We didn't do any shore excursions in Nassau, so I can't help you there. Sorry. Feel free to email me with any more specific questions. I think my email is listed on the forum.