Fort Lauderdale to Port of Miami is about 30 minutes. I have lived here my whole life (42) I would hire a driver my guess $65.00. Your cruise line may have transportation for you. I would inquirer. Taxis are ridiculous.
Fort Lauderdale/Hollywood International Airport (FLL) is about 30 to 45 minutes north of the Port of Miami. Carnival sells transfers for $15/person each way. Typical cab fare is $50 each way for the entire cab (up to five passengers).
Check out www.floridalimo.com
You can get a towncar to take you to the port or your hotel for $55 for up to 5 people. They also have a ride share program where you can wait up to 30 minutes to see if anyone else wants to go to the same place for $15/pp.
We took the cruise transport/buses back to the airport because the pier is a mad house on embarkation/debarkation day. Finding a cab or any other non prearranged transportation wouldn't be a nice way to end your vacation at all.