It is called "visa exempt" and for Australians you now get stamped for 60 days when going thru airport immigration. Using the phrase "on arrival" is problematic as there is a totally separate thing called "visa on arrival" which is an actual visa that lasts 15 days which you apply for when you land but is not open to Australians (or any Anglo-countries) and has nothing to do with your situation. You are not getting a visa. You will just stamped when presenting your passport with a stamp entitling you to stay for 60 days. So your agent is misinformed.
It means you have to get a tax # and pay tax on income brought in to the country. Your assumption on double taxation hinges on whether a double taxation treaty exists between Thailand and the other jurisdiction in which you are paying tax.
Did you originally enter on a Tourist Visa or did you enter Visa Free? If it was the latter it definitely wouldn't be totally unheard of as that would be 4th visa free entry and you would have been looking at near 8 months of continuous living on visa free entry and extensions. And you didn't really say what was going on last year so if you were in Thailand end of last year that looks even worse.