Are there palm trees in Australia?

Im doing a project where we have to invent our own country. And I want mine to be really tropical.. but I want it to be where Australia is. Is there palm tree's there?

Also, any suggestions on where would be a better place to make my "tropical country"? lol.
Update: Thank you very much! :D
My countries gonna be where Australia is.. Im still thinking of a name for my country though.. lol. Any ideas?
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