I have ticketed many DONE's ex-CAI & ex-AMM using Emeco, AA's ticket agent in Egypt. They are very reliable, accommodating & easy to work with.

The easiest way to be sure: call AA RTW desk in US & ask if it is ticketed, and to check that all the segments appear to be in order. As others have alluded, make sure you have your ticket # available (I try to print out the itinerary AA RTW desk will email which has the ticket # at the bottom). The ticket # can become very valuable with OW partners if one is in a foreign land & they can't pull up your reservation with the flight # & date. I had this happen with a LAN flight in AKL several years ago -- it was a nightmare, it may have been something to do with the recent earthquake in SCL.
Remember, certain changes to the ticket (i.e., I believe eVIP's) generate a new ticket # which is good to have on hand.