Yes, car rental is the most economical way to get to Ft. Lauderdale via the Florida Turnpike (the most expeditious way).
As mentioned before, it is about a 3 1/2 hour drive through relatively boring landscapes but you'll easily find the well marked port (just past the airport entrance). You'll have to enter the port through a security gate that insures only passengers and delivery people can enter the "secure" area.
The ships all arrive fairly early in the morning but they must first disembark all the previous passengers and tidy up the ship for the oncoming passengers. Typically, the ships have completed their disembarkation by 10:00 am and if you happen to be there at that time, you may board and enjoy a leisurely time getting to know the ship as it won't depart until late afternoon. The most heavy boarding time is usually between 12:00 - 2:00 pm but sometimes there are air traffic delays (weather related) causing many inbound flights to be delayed and if there is a sufficient number of passengers on these late flights, I've seen the cruise line delay departure into the late hours of the evening. They don't want a huge glut of disgruntled passengers and loss of income by leaving 500-1000 people behind but then again, they won't wait for 10 people if they have a nearly full ship at departure time!
If you leave Orlando at 7 - 8:00 am, you'll be there in plenty of time and then can enjoy the buffet lunch that will be likely offered somewhere on the ship! Enjoy and have the time of your life, most people who cruise enjoy it so much they often forsake a land vacation for yet another cruise.