Yes it probably costs that much for the university, however all domestic places at UNSW are supported by the commonwealth government (hence
Commonwealth
Supported
Place) of which they pay the large majority of your tuition no questions asked. The rest you cover with HECS.
2021 Commonwealth contribution amounts and maximum student contribution amounts by discipline.
www.dese.gov.au
You can see here that the maximum student contribution amount (SCA) a university can charge $11,300, and the government covers the rest with $27, 000 (btw this $11,300 is also listed on the UNSW Future Students Page)
The UNSW website that says 1000 /unit is for *fee* paying students, or students without a CSP, aka International students.