Do. Not. Take. The. Exam. Until. You. Are. Ready.
If YOU don't think you will be ready due to lack of time, lack of studying, or whatever it is, YOU DO NOT TAKE IT.
Some schools take the most recent, highest, or average of the exams. If your first DAT score that you took while you were unprepared was low, you can say good bye to the schools that take averages (unless your retake is very high). Why gamble? This is also precisely the reason why you don't just take the exam to see how it is and also the reason why ALL prep courses and materials tell you not to take the exam until you are ready. You do NOT want to take the exam more than once. Keep that in your mind while studying.
The cost of one DAT exam is CHEAP compared to what you would have to face in case of a terrible score. Wasted application fees (and more if first cycle doesn't go well due to weak DAT score), wasted time with more EC and other things to improve on (many schools want you to improve your stats for second+ rounds of application), and wasted effort. The money wasted would now be in thousands of dollars.
Point is, take the exam when you feel comfortable with the materials and ready to take the exam. Only YOU know whether you would be ready or not by the end of the month. We don't know your study habits, schedules, or mentality.
Also, why Kaplan? Do you think it is helping you? I found Kaplan to be terrible. There are so many other good sources out there. I only used Kaplan for some PAT practices.