I submitted my application and my son's at the same time, with a separate form and birth certificate for him. You can download the form from the Embassy website (needs to be the form from the Embassy in Jakarta), which saves a lot of time.
In Jakarta you can apply for dependents at the same time you submit your own applications. If you submit Monday, you get them back Thursday. But note the Jakarta Embassy is much busier than before - I suggest getting there early to get in the queue. I was there at 8:40 on Monday, was 22nd in line and was seen at 10:20. There was a long line waiting outside when I left.