A week is long enough to see the key sights of Jordan but it's still a pretty hectic itinerary. So don't be expecting long lie-ins or anything!
Highlights for me were Petra (of course) and the majestic Wadi Rum. You'll get most out of Petra if you have a reasonable level of fitness as it's a vast site to cover and many of the best trails and viewpoints requires some (fairly tough) climbing. It can also get blisteringly hot, even when we were there in April, so be sure to wear heaps of sunscreen and a hat. And drink plenty of water.
As long as you're prepared for fairly basic conditions in the desert, you'll have a great time at Wadi Rum. And the food we had there was absolutely delicious!
It would have been nice to have a bit longer in Aqaba (Red Sea) after the rigours of the desert but there wasn't time in the itinerary for that. I can highly recommend the boat trip in Aqaba. We had the entire boat to ourselves (there were only about 10 of us) and both the snorkelling and the lunch they fed us were brilliant. Judging by what those who didn't come on the boat told us, it was definitely the best thing to do in Aqaba.
Amman was a bit of a disappointment ie, a mostly modern city with very few sights of historical interest, but that's fine as it was mostly just a starting and finishing point for the trip.