Wtf no? You can absolutely checkmate an opposing King with just a Queen left, you force the opposing king to the end of the table and then you trap it on a corner by using your own King, since Kings can't get near each other, they have to stay one space away at all times. The opposing King can't retreat anymore and it cannot advance too, then you put your Queen on its flank and ba boom, checkmate.
Although at that point your opponent would resign before you got to do all that.