Sulfotransferase that utilizes 3'-phospho-5'-adenylyl sulfate (PAPS) as sulfonate donor to catalyze the transfer of sulfate to position 6 of internal galactose (Gal) residues of keratan. Cooperates with B4GALT4 and B3GNT7 glycosyltransferases and CHST6 sulfotransferase to construct and elongate disulfated disaccharide unit [->3(6-sulfoGalbeta)1->4(6-sulfoGlcNAcbeta)1->] within keratan sulfate polymer. Has a preference for sulfating keratan sulfate, but it also transfers sulfate to the unsulfated polymer (By similarity). Involved in biosynthesis of phosphacan, a major keratan sulfate proteoglycan in the developing brain (PubMed:24152993). Involved in biosynthesis of 6-sulfoGalbeta-containing O-linked glycans in high endothelial venules of lymph nodes. May act in a synergistic manner with CHST4 to generate sialyl 6',6-disulfo Lewis X motif, a recognition determinant for immune cell receptors implicated in leukocyte trafficking (PubMed:23254996) (By similarity). Catalyzes sulfation of N-acetyllactosamine (LacNAc) oligosaccharides with highest efficiency for sialylated LacNAc structures (By similarity). 3'-phosphoadenylyl sulfate + keratan = adenosine 3',5'-bisphosphate + keratan 6'-sulfate. Glycan metabolism. Broadly expressed with highest levels in central nervous system. Expressed in cortex (at protein level) (PubMed:24152993, PubMed:23254996). Expressed in high endothelial venules in peripheral lymph nodes, mesenteric lymph nodes and Peyer's patches (PubMed:23254996). Expressed in cortex and cerebellum throughout the postnatal period (at protein level). Mutant mice are born at the expected Mendelian rate and have normal developmental and reproductive potential. Belongs to the sulfotransferase 1 family. Gal/GlcNAc/GalNAc subfamily.