I'm pretty sure you can submit the application as soon as it's available to be filled out. I submitted mine on May 18th last year. By the time AADSAS gets your transcripts though, and then verifies the grades, it will be at least June 1st before your stuff goes to schools. Most likely it will be several weeks later than that. Interview offers start to come out around early August (for the faster schools), so you'll want your DAT scores there before than. Otherwise they can't fully evaluate you and they may sit on your app waiting for the scores. I think it's very important to be in that first rush of invites, so get your DAT done by late June. However, if you were planning on studying all summer for it b/c you're not ready, than I'd stick with that plan. Better to have good scores than be extra early. Don't wait any longer than the end of July though. And schedule your test appointment well in advance b/c those dates can fill up.