Looking at Birmingham Airport website the flights to Dubai seem to be operated by Emirates airlines and depart from Terminal 1 but really you should get actual flight information and then check the exact flight on the website or call the airport.
The Dubai flights leave from Terminal 2. All BA flights leave from Terminal 1. Both Terminals are only 100 yards apart. If you are flying with Emirates Airlines they leave T2.
According to the Birmingham Airport website live information Maglet, flights to Dubai departed from terminal 1 last night and again tonight and will do so tomorrow so perhaps Emirates have changed terminals.
Hi JK2, you are probably right as BA are doing a Dubai run as well, I used to work at Birmingham Airport until April of this year, and up till then the Emirates left T2, my apologies if I have confused you, just give BIA a call they will tell you.