When you register on ADA website, you have 6 month period to schedule for the test. Therefore, you can start the process around late Feb or Mar. It takes a week or 2 to get the confirmation letter. Try to get it done early for most convenient scheduling :
When you start the registration process and are confirmed to take the DAT, you can pick a date within a 6 month window. (ie. if I were to register today, I could pick a date between January 6th and June 6th)
Since you want to take the test in August, register sometime in March but you don't need to immediately - you could register in the summer if you want. But to ensure that you test on a specific date of your choosing, it is imperative that you register early to make sure that date is not filled by other testtakers for that test center.
Also you have to have to have a DENTPIN before you register, which in itself takes a few days if I remember correctly.