Don't wait until you take the DAT to submit your AADSAS. Some schools like Nova and Case want your AADSAS done by the end of June. It makes life easier if you can take your DAT before then, but it's not the end of the world.
My best advice as someone who had to reapply because they submitted the AADSAS too late (sept) is to apply early. For some schools it doesn't matter as they don't look at applications until sept, but for some schools if you don't submit in June or July, your chances of landing an interview are reduced.
When you "submit" your DAT scores, all you do is pay for them to be available to the school. When you apply, the school will just download your scores off the web. (which makes it even more annoying that you pay 25/school)