Just sharing my experience in applying Aus visa using ETA last year:
take the chance actually bought the flight ticket then only applied for VISA, have around 4 months ahead of time to get it approved and fly.
Heard cases of not easy getting VISA approved, research around and seek some advice at various forum and group chat. I got it approved within a week with me and my wife and my kid (1 year old)
A note, for the requested supporting i put to the max to avoid any follow up. ie; annual leave approval by superior/company, epf statement, investment in shares, house loan, payslip, all my bank accounts, flight tickets, accommodation details, marriage cert, job letter offer and etc.
Was worried initially but the outcome was positive, the VISA was approved within a week with no hiccups.
So you and your wife and your kids ETA application was not pulled for "additional processing"?