Can a King and Queen mate a King and Knight or is this a drawn game? White has a King and a Queen. 
Black has a King and a Knight.

It is White's move. Can White win or is this ending a draw?
Without any pawns Queen vs Knight endgame is a theoretical win for the Queen.

Actually, most chess sites that have checkmates practice offer this very problem as one of them, along side many other classical ones such as Queen vs Rook, Two Bishops, etc.

Take a look at this mate problem in lichess

The same problem in chess.com

Here is an example of how you can win:

[FEN "8/8/3kn3/8/8/3KQ3/8/8 w - - 0 1"]

1. Kc4 Kd7 2. Qe5 Nc7 3. Qf6 Ne6 4. Kd5 Nc7+
5. Ke5 Nb5 6. Qb6 Nc7 7. Qb7 Kd8 8. Kd6 Ne8+
9. Kc6 Nc7 10. Qxc7+ Ke8 11. Qg7 Kd8 12. Qd7#