If Qatar sent a daily A320 surely that would be viable.
According to Great Circle Mapper the distance from DOH-BFS is approx 3541 miles (yes I know it's not 100% accurate due to winds, detours etc) and the range of an A320 is around 3600 miles depending on various factors.
With 132-144 seats on their A320's surely it wouldn't be that difficult to get a good number of them seats filled without having to make a huge sacrifice for fuel?
Although in saying that some people wouldn't like to fly for ~7.5 hours on an A320 and would probably prefer to use EK or EY in a W/B aircraft from Dublin.