Sulfotransferase that utilizes 3'-phospho-5'-adenylyl sulfate (PAPS) as sulfonate donor to catalyze the transfer of sulfate to position 6 of galactose (Gal) residues of keratan. 3'-phosphoadenylyl sulfate + keratan = adenosine 3',5'-bisphosphate + keratan 6'-sulfate. Belongs to the sulfotransferase 1 family. Gal/GlcNAc/GalNAc subfamily.