There are several forms of sign language; however, in Australia, the language of the Deaf community and the most common sign language is Australian Sign Language or Auslan.
Auslan is a visual, gestural and spatial language that is not a visual representation of English. Therefore, even though a person can be born and educated in Australia, their first language will not be English; it will be Auslan.
Auslan is a language in its own right with linguists having established this through research that began in the 1960s. As noted, it is visual, gestural language that occurs in three-dimensional space and uses signs to represent concepts, in the same way that spoken languages use words to represent concepts. Its grammar and structure bears more similarities to Asian languages than it does to English. It most definitely is not “English on the hands”.
In addition to Auslan, there are other sign language systems which have been used in Australia, particularly in compulsory education. These are mentioned here, so that you are aware of them.
Signed English is a contrived system of signs that follow the grammar and structure of the English language. Whilst some Auslan signs are used in Signed English, it is not a language but rather a visual representation of English. It is used less now in compulsory education, but has been extensively used in Australia during the 1980s and 90s.
Manually Coded English is similar to Signed English; however, it pre-dates it. It too follows the grammar and structure of English, but uses fingerspelling as a means to insert English vocabulary into the signed utterance. Like Signed English, it is a visual form of English and not a language in its own right.
Fingerspelling is the English alphabet in a manual form. Each of the 26 letters of the English alphabet have a specific handshape and English words are spelled out, letter by letter. This is rarely used as a sole communication method as spelling out each and every word is time consuming. Fingerspelling is used in Auslan to express proper nouns, such as names and places.
The most likely sign language that your deaf student will be using is Auslan; however, the best way to know for certain is to ask him or her.