Hi teagan, sorry I didn't see your post earlier, welcome to CruiseReviews! The car seat will be able to be used in the cabs. Beach days or a short island tour would be fine. Your daughter will be a little too young for Camp Carnival, however, I do believe they have some activities for toddlers. If she's not potty trained, she won't be allowed in the pools on board, though.
You could pack the arm floaties, they wouldn't take up much room. However, most every place you go will have life preserves for children. A stroller will definitely come in handy as your little one will get tired with all the walking. As she gets a little older, she'll be able to join in more activities on board and will have more fun. Right now, though, a sand bucket and shovel and she'll be a happy camper. There's no need to pack one, they usually have these type of things on board for a reasonable price. Also, at the beaches you visit.
Don't stress out, go and have a great time, you'll come back addicted!