I was in Key West a couple of months ago and went for the first time a little over a year ago. There are no checkpoints, at least none that I went through, getting to Key West.
The drive is long ~3.5 hours from Miami. It's nice and scenic if you drive in the day time. I drove back at night and almost fell asleep...you cant see much and the ride is repetitive.
When you're there, definitely hit up Duval Street. Always happening. Enjoy.