I have a similar question. I have 14-18 people all arriving at about the same time. Is it cheaper to take taxis, a private shuttle, a public shuttle, rent a van and drop it at the port. I heard you can do that with Hertz (or maybe it was the opposite, that they will pick you up from the port if you're renting from them).
I know $18+tip doesn't sound like much, but I doubt we can get more than 3/taxi with luggage. So that breaks down to roughly a $100 to transport all of us from the airport to the port (ok, that's not terribly expensive either :-)
When in Miami two years ago, we took a shuttle to our motel and the port. The name of the company is Supershuttle. I believe it was $50 each way and the shuttle held up to nine people. You can find them right outside the baggage claim area.
Miami airport taxis have plenty of vans available that can seat approx 6-7, and as Kuki noted it's a flat $18 whether one or six gets in the van. If you have a ton of luggage, there are transport companies in Miami that have small trailers attached to their vans specifically for hauling luggage along with their passengers. I don't have any company names to present to you but try an online search for them.