No, you can register now and take it any day of the week up to a year from now (or 6 months, it is on the website). If you get cold feet, you call and change the date within 48 hours of the test.
I would call now and register because they have to send you things in the mail to complete registration.
Depends on where you are. There is only one prometric test site within a few hours of my school and it tends to be booked. I scheduled my DAT 2 months before I took it. Buddy of mine tried to register a week after me for the same date, but the earliest available time was already two weeks later.
Others may disagree, but I think you should try to register well in advance. Like corolla said, you can reschedule if you feel unprepared. Having a set test date may also encourage you to study better.