Massage is unregulated in Australia, anyone can say they are a massage therapist, no qualifications required.
What Australia does have is massage therapy is recognised by the health insurance funds, they will part pay for someone to have a massage IF you are a recognised provider with appropriate qualifications, professional body membership, public liability insurance and first aid qualifications. If you are NOT a recognised provider, people can't get a part-payment from their health insurance fund and they usually go to someone else. Businesses will generally only employ/contract a massage therapist that is a recognised provider. Even getting the appropriate qualifications, professional body membership, public liability insurance and first aid qualifications doesn't get you recognised by all the funds - a couple of them want you to have extra continuing education AND have been in practice for over 12 or 24 months.
An ITEC Holistic massage diploma is not a recognised qualification in Australia. If you are lucky you might get some recognition for subjects you've already studied, but the level cover in Holistic massage is a LOT less than the Australian Diploma of Remedial Massage that is required for health fund recognition these days. It's pretty much a 1 year qualification and you might get some of the first term subjects waived (term is RPL - recognition of prior learning). Some of the schools you still need to pay for the full diploma and just not turn up for subjects that have been waived, some of them charge by the subject so if they waive any, it is a bit cheaper for you, BUT most of them charge money to assess your qualifications for RPL!
You'd need to bring a lot of details about what was covered in your course. RPL is a HUGE pain. Lots of people just do the whole lot because RPL is so difficult.
If you are moving to a large city in Australia, and have lots of contacts, and have some niche specialty, you could possibly set up a business (still need public liability insurance though), either shop front or mobile, and generate interest without people worrying about health fund part payments, you could do it. Even smaller towns if you have powerful enough niche appeal, eg I know someone in a small mining town, about 15 miles out of town and she does a LOT of Native American shamanic healing plus a bit of massage. People literally travel 100's of miles to see her (basically because the next village along is 150miles away), but if she just did a massage, they wouldn't.