Well, the Queen doesn't really have that sort of power, She has to sign the laws, making them official, which essentially gives her veto power, but the Admiralty does not answer to her, and if she were to seize control (though the QCO would follow her) most Bretonians would be horrified. They are a free people.
Besides that, the QCO is her effort at getting the 'Job done right' and the SF is the traditional fleet...