Taking DAT at the end of sep/early october actually won't matter too much in your case.
Assuming that you e-submit tomorrow, on Aug 27th. At this time, it will take AADSAS at least 4 weeks and up to 8 weeks to process your application, then they will need to send it out to respective schools, which usually takes around 1 wk - 2 wks. This means that your app won't be readily available to schools until somewhere in october the earlest - if you are EXTREMELY lucky and everything goes smooth. Again, I am assuming that you have already sent your transcript and LOR because if not those will further hold up your AADSAS application.
On the other hand, DAT scores usually take about 1 to 2 weeks to reach respective schools, so in the best case scenario they should get to the schools around the same time as your app.