Turkish Airlines has round-trip flights from Houston (IAH) to Doha (DOH) for $799 with a connection. Flights September, October, March, April, and May. Departures on Monday, Tuesday, Wednesday, and Sunday.
Carry-on and checked-bag are allowed without additional fee.
Some small OTAs on Skyscanner have this for about $727, which is cheaper than the published fare. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.