Welcome aboard, Corinda! Your first Disney cruise will be here before you know it! I bet you are very excited!
Port Adventures through Disney Cruise Line are wonderful opportunities to experience some amazing adventures in the various ports of call. Disney works with the tour operators to ensure the very best experience for their guests. However, some Port Adventures have age restrictions. You didn't mention which exact adventures you looked into, but I'm guessing that the age limit on those must have been for maybe six and up, and that is why you were unable to book your little one. Unfortunately, there is really no wiggle room on those age restrictions.
I'd suggest searching for
"Family Adventures" on the Port Adventures page of Disney Cruise Line's website. While not all of these will be for all ages, many will. There will be prices listed for everyone, including ages 0-2, so you will know that your littlest cruiser can join you.
Back on the ship, you will have a fabulous time on Semi-Formal night. Be sure to bring along a nice dress for yourself, a jacket and tie for your husband and dressier outfits for the kids as well. Even the Disney characters will be donning their finest that evening, which makes for some great photo opportunities. Often, this night is also the Captain's Gala night which sometimes means delicious lobster offerings at dinner! You'll have another wonderful Broadway-style DIsney show to attend that evening in the Walt Disney Theatre as well.
Have fun as you continue to plan your first cruise, Corinda. I'm always happy to help if you have further questions before you set sail!