No, your age won't be a problem for being admitted as a PhD student and being granted a student visa, but you may find it difficult to avoid tuition fees.and to win a scholarship to cover your living expenses. Even if you meet the eligibility criteria for such a scholarship, the committee may simply prefer younger candidates, and you won't be able to prove you were discriminated against. However, a professor may be able to fund your scholarship from his grants, but, again, professors generally prefer younger students.
Also, it will be hard for you to pursue an academic career in Australia after you complete your PhD. In order to get a permanent position in an Australian university, you will need to win external grants (e.g., ARC grants), and, again, the committees will prefer younger applicants. If you do not win external grants, you will be an eternal postdoc on short-term contracts (1-2 years), and you will be hired only as long as your PI wins external funding to hire you. Once he fails to do so, you will have to look for another professor who has funds to hire you, and it is not easy at all. It is a miserable and stressful career path.
I lived and worked in Australia and know the Australian academic system. An old Australian postdoc told me that he had wanted to write an ARC grant application and that his boss had said that he (the postdoc) had no chance of succeeding because of the age, even despite that the age is not mentioned in the eligibility requirements. I would advise against trying to start pursuing an academic career in Australia at such an age.