I'm not sure if this is right but here's how I consider it. Consider an acid HA. The equilibrium expression is (A-)/(HA). Here the base is oxidized and the acid is reduced (has a H). Therefore, for an acid you could consider Q to be (oxidized)/(reduced). In a galvanic cell, Q would also be (oxidized)/(reduced), where oxidation occurs in the anode and reduction occurs in the cathode. Therefore, Q = (anode)/(cathode).
But I could be way off base haha.