IMO, you should just wait for the second DAT score to appear on AADSAS before you send your primaries out.
As sjv said, you can actually send the application out if you have your GPA ready. However, they will also send out the previous DAT score. This can be a problem. Some schools won't realize that you are retaking DAT and will start reviewing your application with your previous DAT score. Thus, you will have to notify them all and you need to make sure that they will hold the application until the new DAT score is received.
That being said, I think you should just wait for your second DAT score to be uploaded on AADSAS, since you will want them to wait for the new DAT score anyway....
I don't think being in the first batch put you in a significant advantage than the second or third. However, if you still want to be included in the first batch, you can just take the DAT earlier. 🙂