In theory, Uber is available anytime day and night, but its really dependent on driver availability. FLL is high volume area, so I wouldn't think you'd have any issue. But you could start checking on your app if their are drivers available now for the times that you're interested in to get an idea of availability and cost, just don't finalize pick up. You could also look at Lyft. I travel a lot and haven't ever had an issue getting Uber or Lyft in major cities.