1540s, "management of domestic concerns," perhaps a back-formation from housekeeper.
Entries linking to housekeeping
housekeeper n.
mid-15c., "householder," from house (n.) + keeper. A later equivalent of householder. The sense of "female head domestic servant of a house" is from c. 1600 (to keep house, as part of a wife's duty, is from late 14c.). Housekeep (v.) is from 1842 and appears to be a back-formation.