I would not wait. I would book and lock in the seats, putting one passenger in coach for the shorter DOH-HYD flight. It's only 4 hours and it is not a big waste.
When doing international redemption, it is most important to lock down long-haul flights. You already done the hard part by finding the long-haul ORD-DOH in business class. I wouldn't let the short haul be a bottleneck. If you wait, you could lose the long-haul flight in business.
Also, AA allows free change on dates and routing between oneworld carriers. Keep monitoring availability and see if something better opens up, or if business becomes available on the shorter leg.