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Car rental from Amman Airport to Petra???

I will arrive in Amman by 11:30 pm (for a long conection) and would like to rent a car to go to Petra next day Early morning! Then I have to drive back to the airport by 3pm same day as the flight to Tel Aviv is at 8 pm. Is it dangerous to rent a car to drive from Amman Airport to Petra round trip? What do you advise? What precaution to take? Thank you!!!