It depends on what kind of 19 AA you have. If you have 19s across the board, there's no worries except for the top schools that have averages of 21-22 across the board. But if you have maybe a 23 in QR but a 16 or 17 in RC, that would be cause for concern.
It also depends on if you're applying now or next year to determine if you -should- retake.
For some reason, and correct me if I'm wrong, I feel like the DAT matters more than your GPA without considering upward trends. Of course, some schools clearly indicate that GPA matters more, but this is my theory.
The DAT is supposedly a "standardized test". We all know that's not completely true considering different people who studied different materials took different tests. However, if you compare it to every student's GPA from the thousands of 4-year universities across the nation, DAT is definitely more standardized. In fact, dschools aren't stupid. They know that a 3.9 at a certain institution from a certain program isn't as impressive as maybe a 3.5 from another institution.
Now, whether you believe that your school/program is hard or easy is up to you to decide.
All that I'm saying is you know that your DAT is "average". If you truly think that you had to work for a 3.9 in comparison to some guy who cruised through with a 3.9 (natural talent aside), then you don't need a retake. But if you're even the slightest bit worried and know that you'll regret not retaking if you somehow don't get admitted, then retake it by all means. A 3.9 doesn't look right with a 19 AA for a reason. You clearly have the ability to get 20+, so why not right?