Bonjour Claire,
Je suis Jolanda Koopman de Hollande et j’ habite en Petra Jordanie depuis mai 2015. Depuis le printemps j’en ai là un B&B. Je tiens à répondre à vos questions en Anglais.
From my experience and from what I hear from friends living in ande around Amman in the North and the tourists I had as guests at the B&b last months, it is safe to travel in Jordan. It is easy to hire a rental car and drive yourself along the highlights Jordan offers!
For an week your itinerary sounds good. I would suggest to rent a car at the airport and drive to
Day 1: arrive QAIA Amman, hire car, transfer to Madaba
Day 2: visit Madaba and the Dead Sea, Little Petra, overnight in Petra
Day 3: visit Petra
Day 4: visit Petra
Day 5: drive to Aqaba
Day 7: transfer to Madaba (or stay another night in Aqaba and transfer to QAIA on day 8, depending on departure time).
Day 8:flight back home
Madaba, only half an hour away from the airport. Stay there for example at the Mariam Hotel. Visit the Dead Sea (1 hour drive from Madaba) on the way from Madaba to Petra (another three or three and a half hours from the Dead Sea) and visit Little Petra and three days Petra if you are really in to ancient cities and hiking (a three day ticket costs =60JD, two days =55JD and one day = 50JD).
Drive from Petra to Aqaba within two hours and enjoy the sea. From Aqaba back to the airport in Amman it is a bit more than 300 km.
August is the hottest month in Jordan. September is still warm but the nights get cooler. Temperatures between 18 and 30 degrees on average. If you have any more questions, feel free to ask!
Ma’as salama, sunny wishes from Petra,
Jolanda
Petra Fig Tree Villa