Can I apply for a 60-day extension as an Australian on a tourist visa to visit my Thai wife?

Here is the general information for 60 days family visit extension, but as Tod mentioned, you better check your local immigration office in advance for their own requirements.

so by saying "I am currently on an extension" I take it you already got the 30 day extension you can get from a free 30 day entry or a 60 day tourist visa entry?

Then you should be able to go to the immigration office and apply for a 60 day "visit thai family" extension.

As a rule because you're getting an extension for a different reason (not tourism anymore) the new extension starts the day you apply for it. SO if you apply early you lose the days on your current extension stamp.

GO to your immigration office with your thai spouse and get the list of requirements from that office for the 60 day extension BEFORE you're going to apply and while you're there confirm they're going to start the extension when you apply not add it on.