The Collaborative International Dictionary of English v.0.48:

Queenship \Queen"ship\, n.
   The state, rank, or dignity of a queen.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

37 Moby Thesaurus words for "queenship":
   baronetcy, barony, caliphate, czardom, dukedom, earldom,
   emperorship, empery, empire, imperialism, kaiserdom, kaisership,
   kinghood, kingship, knight-errantship, knighthood, ladyship,
   lordship, majesty, marquisate, pashadom, princedom, princeship,
   queenhood, rajaship, regnancy, royalty, seignioralty, seigniory,
   sovereignty, sultanate, sultanship, the crown, the throne,
   viscountcy, viscountship, viscounty