What do I need to take to the Koh Samui immigration office to extend my Australian exempt visa?

You will go to the Samui immigration office (at Maenam) to apply for 30 days tourism extension.

Samui accepts extension applications within the last 30 days (technically, you can apply anytime now). But, If I remember right, sometimes (not always) they tell you to come back in the last week for tourism extensions.

Here is the general information for tourism extension. But exact requirements are immigration office specific, you'd better contact Samui IO to check in advance.