Yes, but the very act of moving the king can create a check position. As a queen can move (and check) in 360 degree rotation the only way to capture the queen is if the queen checks the king by moving to a space next to the king. The king could then take the queen to move out of check.
If the opponents Queen has just moved to an adjacent square the King can replace/remove the offending Queen if moving to that square does not leave it in a position where it can be captured in the opponents next move. The King can capture any of the opponents pieces currently residing in an adjacent square after the opponent has completed their move, if doing so will not leave it in check.
Thanks for all your answers and help. My game here makes me want to move my white knight from H3 to F2 so stopping check, but did not know if he takes my Knight if I can take the Queen with the King, being as it is the only piece that could?