I'd be surprised if Africa (a 9 pdr castles 64 gunner) wasn't carrying carronades in 1812 - there had been a general wartime allocation of 2 24 pdr and 6 18 pdr during 1794, mostly reduced with the peace of 1802, but with the subsequent expansion of carronade armament during the middle of the first decade of the 1800s the removal of all guns except 'in the way of the rigging' for liners and except for a pair (or maybe a single shifting gun) each for chase (and optionally) retreat in frigates make the widespread repetition of the 1779 Establishments very unlikely to be generally correct.

12 pdr guns, and even more 9 pdr and 6 pdr guns lacked the ability to carry destructively against hull scantlings to the line of metal, and 24 pdr carronades did better than the 9 pdr, and the 32 pdr carronade better than the 12 pdr. Carronades of course don't carry as well as heavy guns in the same calibre, and are handily overmatched by even the lightest pattern of the gun of common calibre.