I personally have not tried this but, I would go into options and turn of "Quest Tracker" there and then under the Default Blizzard UI turn on automatic quest tracking. I have had an instance where I had to Alt-L to bring up the Blizzard Quest Log to click "Complete Quest " so that I may turn in a quest on the run.
I again am not too sure this will address your question, but, I feel it will work.
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