I would like to visit Australia with my daughter. I am not an Australian citizen, but my daughter is a dual citizen, Australian and Ecuadorian. However, she has never had an Australian passport. Her father lives in Australia. Last time we went to Australia she was not an Australian citizen yet so she was included in my visa. Can I do the same this time? Or what kind of visa does she need?
Your daughter needs to get an Australian passport. Under subsection 29(1) of the Migration Act 1959, the government only has the legal authority to issue visas to non-citizens.
Australian citizens (including dual nationals) should use their Australian passport to enter or depart Australia. While it is theoretically possible for a dual national to enter Australia with a foreign passport with another proof of Australian citizenship once they arrive in Australia, practically airlines will deny boarding to Australian citizens who do not check in with an Australian passport, as they will fail the electronic immigration status check.
The Department's advice to dual nationals is as follows (emphasis added):
Australian citizens entering and leaving Australia
Australian citizens should use their Australian passport to enter and leave Australia.
The Australian Border Force has more information on crossing the border.
If you have a passport from another country, you can use that after you leave Australia.
A passport is the best way to show that you are an Australian citizen. You might still be able to enter Australia if you are an Australian citizen without an Australian passport, but it will be more difficult. The airline might also stop you from boarding a plane to Australia.