As said elsewhere, Qatar flights arrive and depart from the Midfield Satellite Terminal (S-gates), and domestic flights arrive and depart from concourses A and B.
As far as I know, the Satellite terminal has no transfer facilities, all passengers need to take the train to the main terminal. The furthest gates are about 500m from the train stop (+ several flights of escalators).
For transfer international to domestic, there are 2 possibilities:

• for C.I.Q. destinations luggage can be checked through (definitely if you travel on one ticket). In this case, just follow the "Connecting flights to Chiang Mai, Chiang Rai, Phuket, Krabi, Samui, Hat Yai, Trat" signs when you get to the main terminal, you can use transfer immigration.
• for all other domestic destinations (even if travelling on one ticket with the same airline), your luggage can not be checked through, you will need to pass normal immigration, collect your bags and check in again. The same on return.

Domestic security is after the shops and the lounges, and is separate between concourses A and B.

If you're travelling in business with them, I expect you can use the Bangkok Airways domestic lounge.

On you return,as a BA Gold you should be able to use one of the Miracle lounges in the satellite terminal.