Not clear what you need. If you are already in Thailand you do not need a visa. Are you looking for an Extension of Stay based on Marriage. If so, and you have the required funds, then it is easy to do yourself without using an (expensive) agent.
You can it easily yourself. But the Thai Transport office does not understand about the codes on your Australian licence. So you need to go to the website for your Australian Government State and download the list of our codes showing on your Australian licence.
You should not have any problem, but they will put a "Visa Exempt" stamp in your passport rather than a visa on arrival which is not provided for US citizens.