Does anybody know what documentation I will need to get married to a Thai woman while we are in Indonesia?

That totally depends on Indonesian law, which seems to be a bit problematic on this point. You must have a religious marriage, before it can be recorded. And it is problematic if both partners have diferent religions.

The Thai embassy webiste might have more information. Here is some infor from the British embassy: http://ukinindonesia.fco.gov.uk/en/help-for-british-nationals/living-in-indonesia/marriage-in-indonesia