There is little traffic around the South Shuna area, though you can expect to see more cars on the roads on weekends. Many residents of Amman come to the Dead Sea for a weekend getaway. Remember that in Jordan, the weekend runs from Friday to Saturday, and keep that in mind when planning your trip.
If you are going to drive to Petra and other sites, you have two different options. Either way, you will need to go through Amman first. The Desert Highway 15 is a straight route from Amman to Petra. It is the more direct route and will get you there faster. For a scenic alternative, take the King's Highway. This is built on an ancient trade route, and there are several old ruins and fascinating sites to stop at along the way. It will take you longer, but it transforms the drive into a full-on road trip.
The drive along the side of the Dead Sea is also very scenic, and there are a few points along the way where you can get out to take photos. The road hugs the shore and has quite a few twists and turns, so take care, as you will inevitably be sharing it with large tourist buses.
When driving in Jordan, watch out for animals by the side of the road. Camels, donkeys and goats are all common hazards. These are all quite stubborn creatures, and they won't generally move out of the way. You'll have to either drive carefully around them or wait for them to pass. Honking your horn is futile - they may decide to attack!
Always carry cash when traveling in Jordan. Many gas stations, particularly in rural areas, do not accept card payments. The country also has a large number of roadside coffee stalls and fruit sellers. If you want to stop for a snack, you'll need to have some cash handy.
South Shuna is close to the border with Israel. Unlike most countries in the region, Jordan maintains diplomatic relations with Israel, and the border is open. It is guarded, so you don't need to worry about crossing by accident. If you wish to travel between the two countries, be sure to discuss it with your Enterprise Rent-a-Car agent first.
Police and military checkpoints are a common sight in Jordan, often on the outskirts of cities. If you get stopped, the officers will usually ask to see your documentation. Don't panic - this is perfectly normal.