Im taking the DAT in aug, and i don't think its late. just get your application in early, and take your DAT within a month or two from then and i think you should be fine. im sure you already know this, but there is an overlap (aadsass 4-8 weeks, DAT sent usually within a couple of weeks to a month). also, its better to take it a little later and do well then to take it earlier and do bad. my 2 cent.