From the time of the gold rushes of the 1850s to about 1989, most Chinese people who came to Australia were from the southern provinces and spoke Cantonese, Hokkien or Hakka. I can remember seeing Lunar New Year decorations and advertisements saying gong hay fat choy (or variations thereof).
About nine years ago I started teaching at a college which overwhelmingly catered to Chinese students. It being February, I started with gong hay fat choy! and no-one understood me, because they all spoke Mandarin (and/or because my Chinese pronunciation is so bad). Finally one student understood what I was trying to say.
Especially post-Tiananmen Square, more people from the northern provinces came here and Mandarin gradually overtook Cantonese as the most-spoken kind of Chinese. The 2016 Australian census reported that 2.5% of Australians speak Mandarin at home, alongside Cantonese at 1.2%, and Arabic, Vietnamese, Italian and Greek (with between 1.4 and 1% each).
The decorations currently in the Queen Victoria Building say gong xi fa cai, which is the same greeting (approximately “congratulations and be prosperous”) in Mandarin. This is written in traditional characters 恭喜發財 for Cantonese and simplified characters 恭喜发财 for Mandarin. Wikipedia gives the transliterations gōng xǐ fā cái for Mandarin, Gung1 hei2 faat3 coi4 for Cantonese, Kiong hee huat chai for Hokkien and Gung hee fatt choi for Hakka. (But note that the differences between kinds of Chinese go beyond pronunciation.)
Elsewhere, other shops have English only, or various greetings in Chinese characters, including 新年快樂 (traditional) / 新年快乐 (simplified), which is simply “happy new year”.
Note that the decorations, and this blog post, use “lunar new year”, and not “Chinese new year”, which Wikipedia uses. Lunar new year is celebrated in other east and south-east Asian countries, even if they got the idea from China. Other countries also independently developed a lunar new year in late winter/early spring, and there are other lunar new years at other times of the year.
If we say “lunar new year”, what do we call 1 January? “Solar new year” doesn’t sound right. Sometimes I’ve said to students “modern international new year”, but that’s a mouthful.
I drafted the above before I went to work. I had an idea to ask a Chinese colleague about the pronunciation (I know that the transliterations x and c are unusual sounds for English speakers), in case I had any Chinese students. I didn’t ask her, and I did have two students from China, so I couldn’t greet them with this. Then after class, as I was finalising a few administrative tasks, the cleaner, who I haven’t met before but who is obviously Chinese, poked her head around the office door and said that she had finished, could I please lock up. Of course, I couldn’t say this to her, either.