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He also told a news conference in Berlin that planemaker Airbus was on schedule to deliver its first A350 to Qatar "towards the end of this year".
Qatar Airways is the launch customer for Europe's new mid-sized passenger jet, with 80 A350s on order.
It has also ordered 10 of the larger A380s and says it has a total of 300 Airbus and Boeing jets on order, including options.
Al Baker, who has previously criticized the reliability of the 787 Dreamliner, said the airline continued to have "issues" with Boeing's latest airplane but described them as normal teething troubles for a new model.
He was speaking at the world's largest tourism fair, where the airline unveiled its A380 offering including wireless Internet and what it says will be the industry's widest first-class seats, supplied by B/E Aerospace.
Qatar Airways also said it will be flying to a new destination, Tokyo's Haneda, on top of six routes already announced for this year including Philadelphia, Dallas and Miami in the United States.
It recently said it will start all-business class travel between London and Doha on an Airbus A319, a premium service that Al Baker joked would "not be cheap".
Al Baker confirmed Qatar has applied to be allowed to set up pre-clearance faciltifacilitieses to screen passengers heading for U.S. airports from its new Hamad International in Doha, echoing a practice recently adopted in the United Arab Emirates.
U.S. pilots oppose the trend towards pre-clearance, saying it puts competing Gulf airlines at an advantage. Al Baker dismissed the criticism, saying the pilots "should not complain about facilities that are in the interest of their country".
He said the delayed opening of Qatar's new Doha airport would happen soon, starting with low-cost carriers and those without onward connections, and that he believed it would be running by the time Qatar hosts an airlines meeting in June.
(Reporting by Tim Hepher and Victoria Bryan; Editing by Louise Ireland)
