Ok on my first take of the DAT my QR was a 15. So because of that I have been working a lot harder on increasing my QR score.
One tool will help you more than any other. Math Destroyer. My recommendation would be to get it. Go through each test without a time limit, one page at a time--then look at the answers for that page. Any problems that you had absolutely no clue on--bust out your white board and practice doing them and setting them up after you read and understand the solution. You will learn a ton and a lot of the same stuff will show up again and again as you run through the tests.
Towards the end the first time through (tests 8,9,10,11) I started timing myself just to speed up the process. I was surprised at how much faster i could set up the equations from the word problems and how "age" "combined work" and probability problems scared me less and less the more I did them. I still did not have enough time, but the ones I missed i reviewed and learned from my mistakes.
So far the 2nd time through I have been timing myself. I got one of those little minute timer thingies and only give myself 45 minutes for each test. If I look at a problem and do not know how to set it up in 10 seconds, I mark and move on, coming back to it at the end (practice for the real thing). I was impressed with how I remembered problem setups on the 2nd time through so much more, and how much that fear of certain problem types was gone. Go through all the tests a 2nd time, timed...and you will score so much higher. I got a 19 on the last topscore I took.
Last word of advice: Khan academy. Look it up on google. If you want a refresher on any math concepts he is the man for quick, easy to understand tutorials on any trig or math problem. Like for me, solving and graphing absolute inequalities always gave me a hard time. Khan had 3 10 minute videos explaining exactly what i needed to know. I have used his resource for age problems, absolute value, function inside function problems and a lot more. The key with Khan academy is to hit ctrl-F and search for whatever you need to work on.
Sorry this was a little long winded. The bottom line is the kind of questions they throw at you on the QR section are special and often times unique to this test. Spending a semester or more on a regular trig class will not help you as much as the 2 resources I mentioned for DAT QR problems.
I wish you good luck. From one who literally almost cried the first time he took the DAT QR section--believe me it gets so much better with the right practice.