I agree that July-August is a great time to take the OAT. That also gives you time to re-take it in the fall if need be. You have to register online to take the OAT before you can actually schedule your testing date with a testing center. You can register now and pay the fee, and then schedule at your leisure.
Here is the website where you register:
http://www.ada.org/OAT/register.asp
I scheduled my OAT date about two weeks in advance with no problems, however I took it at a less busy testing time (in October). You can look at available testing dates and times online without actually scheduling (you will have to enter your registration information) and see how the time slots are filling up at your testing center. If your testing center is very busy and you are taking it during the summer, you probably want to schedule it at least a month in advance, maybe more.