Food. The restaurants in Petra can be pretty wretched. Although you are officially not allowed to bring water across the border (and some say food as well), try smuggling in or purchasing there a few snacks to tide you over and skip the lunch.
Good shoes. Many lovely European women were shod in white bobby socks and sandals, but to get off the main path (and even sometimes on it) you need a stout pair of shoes.
Layer. From one side of Petra to the next you'll experience temperature fluctuation and a wind chill.
Necessary rooms. There are toilets available throughout the park, but the deeper you enter the less kept up. Bring your own tissue.
Animals. Carriage rides are $30 for two passengers, camels are $15 and donkeys $10. A free horse ride up part of the hill is included in your admission. The ascent takes 20-45 minutes, depending on your physical abilities, so a conveyance may not be a bad way to maximize your time.