All of what I am about to say will give you the best shot with your application to dental school, however, please note that many, many people get in even when they submit their application at a later date. Generally, it is best to have your application submitted by mid-August.
Here is what I would suggest, because it worked well for me...
Apply right away in June. AADSAS usually opens the application at the very beginning of June (June 4th this past year), and that's the earliest you can begin your application. Try to have your application completed by the end of June so that you will (hopefully) begin to receive interview invitations in early August.
You SHOULD submit your application in June, even if you have not yet taken your DAT!!!
It takes AADSAS about 3 weeks to process your application. After it is processed, AADSAS will send your application to your chosen dental schools. Once your DAT scores come in, AADSAS can immediately forward those to the schools as well, but only if your application has already been processed.
So between now and June, try to get all of your letters of recommendation set. A committee letter works if your school has a letter writing committee. Otherwise, you can submit 4 individual letters of recommendation to AADSAS. I would suggest a 1) Biology Professor, 2) Chemistry Professor, 3) Non-science Professor, and 4) Dentist you've shadowed. Every school has slightly different letter of recommendation requirements, but this set of 4 worked for the 10+ schools I applied to.
You can also begin to draft your personal statement, where you describe your personal and professional goals, your motivation for dentistry, what inspires you, random other stuff that makes you unique, etc. in less then 4500 characters (not 4500 words). There is no standard format for the personal statement.
One last note (sorry about this book of an answer), I would suggest that you take your DAT earlier (June) rather than later (July) because you have to wait 90 days if you need to retake. I took mine in April just to be safe, but luckily I didn't need a retake.
Good Luck!