We are visiting this area during our trip to Australia in October. Although I understand it will be quite warm during the day, does one wear shorts or cool pants (to protect the legs from sun, flies, etc.)?

Flies may be a problem in October. I would be prepared to wear lightweight long pants and shirts, as well as a brimmed hat from which you can hang some fly netting.

Or get a hat that hanging corks that swing back-n-forth that hopefully will keep the flies away.

The flies are most annoying. Flicking them away is the unofficial salute in Australia.

One thing I remember from visiting the Ayers Rock area is the fine red dust that gets into everything. I'd avoid wearing anything that is white that you can't live without back home, 'cos it might not be so white when you leave. The sun here in Australia seems to be stronger than the sun in other parts of the world, so put on a high factor sunscreen on any exposed skin.
Kay

Good point about the dust. Your clothes will take a bit of a beating. Long sleeves and long pants are a good idea - perhaps shop at a charity shop for clothes you can throw away afterwards - makes room for souvenir shopping.

Thanks to all! We'll be prepared.