Involved in the biosynthesis of (+)-O-methylkolavelool. Catalyzes the addition of a methoxy group to the C-13 position via the transfer of a methyl group from S-adenosyl-L-methionine to (+)-kolavelool to form (+)-O-methylkolavelooldaunorubicin. (+)-kolavelool + S-adenosyl-L-methionine = (+)-O-methylkolavelool + H(+) + S-adenosyl-L-homocysteine Belongs to the methyltransferase superfamily.