Welcome to cruisemates. Oh, what fun to plan your first cruise. I would suggest Carnival for a first cruise, especially with a child. Carnival has an excellent day care program for children. You'll be able to sign your daughter up the first day on board. You'll have plenty of time with her and for yourselves.
As for where to go, I think maybe the Western Caribbean would be a nice fit for you as you'd be able to look at the ruinn in Tulum and swim with the stingrays in Grand Cayman or ride the horses. May I suggest that you sign up at the Carnival website and look around there and see what they have? You'll be able to see what kinds of shore excursions they offer, too. I would suggest that, as newbies, you take the cruiselines shore exsursions. And, I like to stick with at least a seven day cruise. I think Florida would be a great place to leave for you, and Miami probably might be ideal for you since you have a place to stay.
Enjoy planning! We'll be here to help!