I took my DAT the first week in June, I think the 7th actually. This is a good time to take it because it gives you about a month to study after final exams. You are able to apply without your DAT, but I waited and sent my application in the beginning of July, but could have done that earlier. I spent a couple of weeks celebrating my DAT score instead of working on the application.
I started receiving interviews the first week in August and I received three or four, and the rest followed the next month or so. My interviews were scheduled different times, two in september, three in october, one in november, and one in december. I withdrew one of my apps for an October interview, and was accepted to three schools december first so I withdrew my app for the decmeber interview.
Hope this helps.