Yes it's too early to fill out aadsas. From what others have said in the past, your application will be deleted at the end of this cycle and you'll have to open a new one on May 15th (or whatever the opening date is for the next cycle this year).
I wouldn't send your official transcripts to aadsas until right around May 15th... they have to be official copies from your schools. LOR would be fine to get now (my school has a LOR collection service so it was really easy).
Register for the DAT whenever you're ready. Your official scores get sent out by a different group than AADSAS so they're not really connected.