It should be possible to apply for academic studies in Australian with just a TOEFL score. The university should probably not have a big problem with this.
But you still need to sit for the IELTS exam — it is a requirement for the academic student visa.
To quote from the immigration website:
The Student Visa Regulations require students to have sat an International English Language Testing System (IELTS) test prior to lodging their application.
Source: http://www.immi.gov.au/students/english-requirements.htm