i'm going to assume you're setting sail from port of miami, and not port everglades (which is in ft lauderdale). lots of people assume they're the same thing...
there's tons of places to see and bring your daughter, and it's not all as touristy as you think. most of the suggestions i'll make will be outdoorsy type because the weather is generally better and i'll focus around the fact you've got your daughter with you
at that time of the year, we're beginning to see summer lite, so the weather is a bit nicer than the sweltering heat we get in the summer.
downtown miami is extremely safe, as nothing happens there after 5pm that you'd bring your daughter to (except for when there's an event at the Arena such as a Heat game or a concert). even the bums have mostly been moved out. i wouldn't visit downtown miami as an attraction as it's mostly offices and duty free shops for international travelers. there's Bayside, but with the exception of the terriby touristy bout tours, i wouldn't waste my time.
i'd spend more time at the beach itself (south beach isn't that bad), as you'll see a ton of different types of cafes and people watching can be VERY entertaining. or you can just cruise through. stick to daytime visits and you'll be fine. i wouldn't go there after dark with your daughter, as it's a more "adult" clubbing type crowd. also near the beach you'll find Parrot Jungle Island and the Children's Museum of Science (both on what used to be watson island). they're on the infamous causeway where will smith and martin lawrence had a chase scene in bad boys. nice place to drive through and you'll get to see where all the cruise ships port.
Parrot Jungle Island is basically a giant aviary. it's pretty cool, and kids love it, plus it's right on the causeway from the beach. i take my niece there and she always has a good time with all the wildlife. http://www.jungleisland.com/index.cfm
the other beach that's very popular would be out in Key Biscayne. You get to enjoy the miami skyline, and since it's on the bay, the water is VERY shallow, which kids love. if you make it out that way you can visit Crandon Park. there's all kinds of activities out there (kayaking, sailing, windsurfing, eco tours, nature trails, etc), and you'll see a very active community if you go out there. http://www.miamidade.gov/parks/parks/crandon_beach.asp
if you make it out to Key Biscayne, i would NOT visit the Miami Seaquarium. it's terribly expensive and the facilities are in awful shape. don't let anyone else tell you otherwise.
also in that area you'll find the museum of science and planetarium. very cool place for kids, and the planetarium is just awesome. they'll even have laser shows at night and you can hit up the observatory at night to check out the stars with their telescope(s). http://www.miamisci.org/
right next to the planetarium is the Vizcaya museum. it's a historic landmark built in the early 1900s with some very cool gardens and grounds. it's where our annual renaissance fair is held. http://www.vizcayamuseum.org/
about 30-40 minutes south, you'll find Monkey Jungle and other landmarks such as the Shnebly Winery, Knaus Berry Farm, and Zoo Miami. (yes, even more animals.)
Shnebly Winery is a full-on winery with interesting wines such as guava, mango, and other tropical tasting wine fusions. you can take the tour and have a wine tasting. http://schneblywinery.com/
the Knaus Berry Farm is fun because you can pick your own strawberries if you like, but the best part is the home-spun milkshakes the make with the berries and the amazing sticky buns. this place gets VERY crowded during the season, so plan to be there early. http://www.knausberryfarm.com/
Monkey Jungle is just what it says; a zoo focusing on monkeys. it's neat because you walk through a covered walkway with primates all around. kids love this, too. http://www.monkeyjungle.com/
Zoo miami is sort of self explanatory. your daughter can feed and pet giraffes there and see other wildlife. http://www.miamimetrozoo.com/
Also down south is the Homestead Speedway. Sometimes there's neat tours and weekend events going on that might coincide with your stay. http://www.homesteadmiamispeedway.com
And even further south is the Florida Keys. you can do all kinds of stuff like charter a boat and go fishing, swim with the dolphins, enjoy a beach, etc. just google florida keys.
additionally, out to the west is the Florida Everglades. if you jump on Tamiami Trail and just head west, there's TONS of alligator wrestling, airboat tours, and native american settlements you can visit. one really cool place we frequent is Shark Valley. it's a 15 mile loop with an observation tower out in the everglades. you can either rent some bikes and do the loop, or jump on the trolley that takes you through it. this time of year you'll see PLENTY of gators out on the trail because they leave the swamp to warm up on the paved bike trail. your kid will probably get a kick out of that. http://www.sharkvalleytramtours.com/
There's also a ton of places to eat with all kinds of influence. make sure you guys hit up a cuban place (they're hard to miss... it IS miami, after all). i'd recommend Versailles (how's your spanish?), La Carreta, or Sergio's, but really almost any cuban place will do (those 2 are just landmarks).
What is your date range? i can probably find out what date-specific events are going on if you'd like to go see a show or a sporting event or something like that.
what other kinds of things are you into? it's pretty much snowbird season at that time, so there's TONS to do.