Submit your app early! Register with AADSAS, complete your app in its entirety, and on the DAT page, just put in July 2006 under future test date...that will allow you to submit the app without having taken the DAT yet. Do not wait!
Take the DAT in July, and send in the score reports to the schools as they require it, also follow up with AADSAS and make sure they receive your scores.
Sidenote for the last poster - yes, you can take the DAT anyday of the year, even tomorrow if you want to. Before or after the application, doesn't matter...preferrably before so that you have everything together when you submit and won't have to worry about tracking things down later.
Indy