Flights at this price can be found starting in late September and valid on Tuesdays, Wednesdays, and Saturdays through February 13, 2019.
There are a few flights per day by American on this route, so you shouldn't have much trouble piecing together an itinerary that works for you.
This fare books into American's Basic Economy fare bucket, but they no longer limit you to a small personal item, basic economy has opened up to allow for that standard sized carry-on like the good old days.
Need a place to rest your head in the Big Easy? Here's a list of available accommodations for the sample dates on Hotelwatchdog.