If you come from the US you may find this experience frustrating, but this is standard operating mode elsewhere in the world. We don't have a general policy of being able to do same day change like is common in the US. And because it's not a normal thing, the frontline staff are probably not trained up to do it.

If you had asked to do a flight change at Doha (I.e. A hub airport with airline direct employees all over the place), whilst it might not have been free, they would have had someone who probably could have facilitated the request at a cost. But you have to appreciate that you're at an outstation, all the staff apart from the station manager are contractors. They might be wearing a Qatar uniform, but after their shift they have a break and then go and wear a different uniform for the next flight.

As the poster above notes, the fact that this was an AA ticket complicates things for voluntary changes once a flight is open for check in, as Qatar will only want to make changes for IRROPS but AA have lost control of the ticket because it's under airport control. Award ticket makes it double complicated as there's no hard currency monetary value to use towards the rebooking.

There's also a cultural thing going on as well. As an employee in the Middle East you do what you're told to, and tread carefully when you have the opportunity to move outside of those boundaries. Management's view of employees going the extra mile to do something unusual or exceptional for a customer will typically be viewed as doing something they shouldn't. Unless the customer was super important, then a dim view is usually taken and it can result in the termination of the employee's contract. If you were an employee on the check-in counter working under these parameters and you are given the opportunity to do something beyond checking a customer in for the flight that is open for check in, what would you do?