There are two typical antidotes to this problem:
1) Get good at endgames, so that a trade of Queen-for-Queen puts you right in your comfort zone. Then your opponent is just playing into your hands by offering a Queen trade.
2) Use your Queen as a support piece (like Artillery) instead of trying to use it to spearhead the attack. He can't trade it off if you haven't exposed it.
1 is probably better, I find that most times a side cant force a queen exchange without entering an endgame in which he had to make some concessions.
Who has won over half his games!!!!!
Are you more concerned about improving , or a rating?