You may also consider:
Sri Lankan Airline with stopover in Colombo
Cathay Pacific with stopover in Hong Kong
Royal Jordanian with stopover in Amman
if you wish to explore the Middle East I would much prefer Amman over Doha. Doha is fine for half a day. From Amman you can visit Petra or Jerash. You can even go to Jerusalem but factor in time to cross the border.