Former drywaller here...other than furring out and attaching the drywall to wood, laminating the drywall to the brick will be iffy, but it can be done. It's much easier to show someone how to do this than to write it out, but here goes... First, clean the surface of the brick by brushing hard with just a bristle brush, then scrub a bit with some water. Doesn't have to be clean enough to eat off of, but just to minimize loose gritty or powdery stuff. Make sure no little chunks are loose to fall into the way later. Murphy's law takes precedence over everything but God and gravity. Get the kind of construction adhesive -- the good stuff, not Liquid Nails. Use "stand-ups," long pieces floor-to-ceiling, rather than stacking 4'-wide ones. Try to mark the mortar lines on the rock as best as you can, since in my experience sometimes brick shatters rather than accepting a nail. When you have the pieces cut and ready to go, put globs on the brick rather than long lines of adhesive for the board to squish into. In my house I used 1" concrete nails to hold 5/8" rock. Push the drywall into the globs until contact with the brick is made, then, holding the rock to the wall so it doesn't start to back off, tap in the nail until it touches, then try to drive it home with one or two solid bangs (I use a 28-oz. shingling hatchet for hanging drywall). If the rock isn't tight to the wall, the vibrations that set up will further loosen it from the glue globs it had contact with, and any nails that have been driven home will likely pop the paper and become ineffective. The glue, not the nails, is what will hold it to the wall. The nails are just to hold it long enough for the glue to set.
It's harder to laminate to brick than to concrete. I've actually used drywall nails successfully for concrete, but in a very particular way. Brick? I hate it.