You could get a tourist visa from the thai consulates in Oz (Canberra or Sydney) and that would get you stamped in for 60 days when you arrive.
Sydney does it all online, you apply, get approved, send your passport, documentation & a post paid envelope and they put the visa in and send it back to you.
OR
You could just show up and get stamped in free for 30 days on what's called a visa exempt entry, then extend that by 30 more days at the immigration office (NOT the airport) after you're here for 1900baht.
Honestly getting the single entry tourist visa from Sydney is the way to go as it's only 1400 (AU 60) to get the tourist visa where it's 1900baht to get the extension after you're here
This is the link for the single entry tourist visa from the Sydney thai consulate
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