i'm in the same boat as you... i'm going to be taking my dat by the 1st week of June. I plan on working on my LOR, personal statement and all that to have it done before the end of March/ April. Once the application opens in May, I'm going to work on it asap and have it completed before the end of May so the only thing left is my dat scores and waiting for my exit transcript from my school.
If you wait til June to take the dat, make sure you take it early june and you have everything else completed and ready to go...
-ld