Hey,
I've just finished my first year studying mathematics at the ANU, also originally from NSW, and completed MATH1115 earlier this year. The lecture notes that are provided by the lecturers would definitely suffice to do well in the course, but they do recommend buying the two prescribed textbooks for the linear algebra and calculus halves of the course. The linear algebra textbook (Elementary Linear Algebra - Anton and Rorres) is probably more essential to get instead of the calculus textbook (Essential Calculus - Stewart) as MATH1115 assumes quite a bit of linear algebra knowledge that isn't covered in the HSC in NSW, and the lecturer required us to read certain chapters from this textbook before starting the course. However, both textbooks are more for practicing computational examples related to concepts in linear algebra and calculus, which is not the aim of the course as MATH1115 is very proof heavy, unlike maths at the HSC which is why the lecture notes are generally better study aids compared to the textbooks. But I recommend getting the linear algebra textbook (assuming they don't change the prescribed texts for next year) as NSW students have much less experience with linear algebra compared to ACT students.
Hope this helps.