Hasn't QR come out and said that problems with the 787 has caused delays with starting new routes which the 787 will be used on?
No, apart from Chengdu and Chicago:
Qatar’s planned daily non-stop Doha-Chicago O’Hare service, slated to get underway on April 10, will initially be operated only 3X-weekly, the airline said. However, the carrier said it will increase to the planned daily frequency from June 15.
Additionally, the launch of 3X-weekly flights between Doha and Chengdu (in central China), which was intended to start on March 19, has been postponed indefinitely.
The announcements come as the carrier works to adjust capacity on existing routes as a result of the grounding of its Dreamliners.
They have not issued even a provisional launch date yet either for BHX, only this:
“We can confirm we are planning to launch passenger flights to Birmingham, but are not yet in a position to announce a date nor schedules.
We mustn't also lose track of the fact, without aircraft leaving the fleet, the B787 comprises only 4% of Qatar's fleet.