Specifically dimethylates two adjacent adenosines in the loop of a conserved hairpin near the 3'-end of 18S rRNA in the 40S particle. adenosine(1779)/adenosine(1780) in 18S rRNA + 4 S-adenosyl-L-methionine = 4 H(+) + N(6)-dimethyladenosine(1779)/N(6)-dimethyladenosine(1780) in 18S rRNA + 4 S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. rRNA adenine N(6)-methyltransferase family.