We are doing a quick trip to Jordan in early October, arrival on the 8th mid-day and departure on the evening of 12th.

Our plan is to get to the dead sea on the arrival day, leave to Petra the next day and spend time at Petra and visit Wadi Rum until returning to Amman airport on the 12th. We are not planning to rent a car (unless recommended) but would need the transports to the dead sea, from there to Petra, Wadi Rum and back to Amman airport. Not sure yet if we'd like to spent a night at Wadi Rum and we could go directly from the dead sea to Wadi Rum and visit Petra on the way back.

Any recommendations how to arrange the transports, just book a taxi at the airport/hotel for each leg? A contact for a tour agency that could arrange them? Or rent a car?