Transportation from Orlando airport to Port Canaveral hotel?

There are so many companies that provide transportation to Port Canaveral. If you would like to arrange your transfer ahead of time, i would recommend Star Trans company - http://www.orlandotransportationshuttle.com
I don't know how many people are in your family, but the price for a group up to 4 people will be around $100. Very often they have great deals online.
The second option is Mears. They have a stand inside the airport. You will have to wait for 30-40 min, but no need to book in advance.

Thank you, guys. I think Star Trans will be the best option for us. The rate (for 7 people) is only $115. It is a special summer rate, but even the regular rate ($125) is cheaper then what Disney would charge us for a shared shuttle ($35 per person).

Disney also puts on transportation to the Port Canaveral cruise terminal via its Disney's Magical Express service at Orlando International Airport. Look for the cruise-transfer reps and kiosks once you get through immigration/customs. You'll need to make arrangements through Disney if you want to take this option. Note that there's an additional fee, so make sure to confirm round-trip prices! Here's a link to some additional info: http://bit.ly/3quPfQ