Qatar Airways are one of the most famous international airline operating in almost all famous destinations. I have personally traveled on it and I am satisfied. Its an advantage of using Qatar Airways that you can go to your favorite destination non-stop however you will find Qatar airways bit expensive than other options.
I went to United States (Washington DC airport – IAD) and the cheapest option I got was via British Airways though it was with 2 stops, one at Manama, Bahrain (We just waited inside the plane for an hour) and next flight took stop at London Heathrow. Even Etihad airline and Oman airlines are cheaper than Qatar aiways, Oman airways is not as good as Qatar airways however services of Etihad airline was comparable to Qatar airways.
You can book your tickets online on Qatar airways website however make sure that whoever is using his credit card should have it on his own name or should be there at airport while boarding the plane. If you want to purchase ticket for someone else and not going to airport with him/her then prefer expedia.com as it offers almost same ticket price.
If you want to book online tickets at Qatar airways follow the below mentioned link