From the Australian Home Affairs website, from 6th April, you apply on the Australian ETA app available from the Apple Store or Google Play Store and in most cases you will be notified of the result immediately - Australian ETA
There is no Visa Application Charge (VAC). There may be an application service charge of AUD20.
You will also need a NZeTA - NZ ETA
For a NZeTA -
Cost and processing time
Requesting an NZeTA costs NZD $9 through the app or NZD $12 if you use the online form
Allow up to 72 hours for processing, although it could take as little as 10 minutes.
The IVL
If you are entering New Zealand you must also pay an IVL, which funds tourism infrastructure and helps protect our natural environment. You pay the IVL at the same time as you request your NZeTA. The IVL costs NZD $35.
As long as you don't need to renew or replace your passport, you can obtain your ETA or NZeTA anytime I believe. But do check the websites for the information required.