Is the DAU course registration done automatically when I get the course approved on my IDP?

No. Your application must be submitted via AITAS. AITAS is interfaced with the IDP system but it is a separate system. The DAU course(s) you are applying for must show APPROVED status on your IDP at the time you start the AITAS application process. A link to AITAS is provided under the ìDAUî category on the planning page of your IDP and is https://www.atrrs.army.mil/aitas/.