We will arrive in Petra late, around 1:30 am. Not sure why all the flights I found arrive so late. We will stay that night and the next in Amman to rest and do a little sight seeing. We will leave early the next day to go to Petra and stay the night there, going directly to the airport to catch a flight to cairo. Besides being very busy, is this do able? Would people suggest renting a private car/taxi? I have read about the buses and they seem reliable, but we can't miss our flight to Cairo. Thank you for any help.