For Boeing training you have many options:
1) In house in Doha, STAR course mostly.
2) Gatwick or Singapore, Full Course with Boeing instructors then QR OCC back in Doha.
3) Same as above, but short course with QR instructors.
Regarding DEC coming from NG, for as much as I know they just closed the application. If you have passed the assessment you should be ok on the 787.