I believe Lonely Planet is correct. It's pretty much a resort town and people are generally picked up by their hotels. You can rent a car though.

Also, note that you'll also need to pay a park entry fee, I think to get close enough to the rock.

You'd be pushing for time too. Assuming you land on time, and get out of the airport by 12, you'll only have an hour or so and be back at the airport by 1pm.

There're several flights leaving around that time, and you'll need to go through Security.

To be honest, you'll get a better view if you pick a window seat on your inbound flight. I'd a port-side window seat, and the view was great.