How much time do I need to allow from getting off our cruise to leaving on our flight?

If our cruise ends at 6:30am in Fort Lauderdale, FL, on a Thursday, would a 9:00am flight leaving Fort Lauderdale's airport be too soon? What time should I be looking for a flight? First time cruising, so I don't know how long it takes to leave and then also the security checks at the airports. Thanks