Can I use visa exemption upon arrival and then get a tourist visa while returning to Thailand after my trip to Australia?

Get the tourist visa in Australia, it's cheaper, less hassle and you'll need onward travel within 30 days for your 2nd visa exempt entry.

Do the 30 days on arrival and a visa extension...

Sounds good to me but Im no expert.

I think u mean to Oz for wedding.

Should that be departure ?

Visa exempt on both, then extend 30 days on your second visit. Long flight to Aus for 6 days by the way!

What country is your passport from? Some countries won't issue visas if you're not a citizen or resident there. If you're not a permanent Australian resident, you should check if you getting a tourist visa there is an option.

If you decide to visa exempt, you may need to show onward travel out of Thailand within 30 days, even if you plan on extending. This can be as simple as a cheap throwaway bus or train ticket out of the country to let you check-in to your flight though.