Draw question

White Queen& King veurses Black Queen & King. Is this a draw or can a player be check mated??

It is still possible for either player to achieve a checkmate.

Have you ever seen the movie Searching for Bobby Fischer which was based on the true story of Josh Waitzkin? The final game at the end of the movie that he won was a fascinating game that simplifies into a Q+K vs Q+K position, but with a decisive victory for Josh. Here is a youtube link that shows the game board moves as the movie plays out the end of the game:
YouTube

Josh's pawn ends up queening after his opponent, but with an immediate skewer of the opposing king and queen.

So yes it can be done, but it's not very common and in most cases would require some naïve help from your opponent making poor moves. The problem is that the moment that you stop checking your opponent in order to reposition your king he can now check your king around the board. Provided you resist moving to the edges and corners of the board as much as possible it's very hard to get checkmated because he needs to move his king to force you to the edge and then you can check him with your queen and now the roles reverse.