Perth airport offers the cheapest routes to Bangkok, from ฿9,033; whereas Melbourne airport is typically cheaper if you're flying to Bangkok, from ฿10,007. It's best to make sure you are flexible on dates to find the cheapest possible flight options for your journey.
Here are some of the cheapest flight destinations from Australia:
Fly from Perth to Bangkok from ฿9,033
Fly from Melbourne to Phuket City from ฿10,007