If my wife of thai nationality has a baby born in Australia what rights does the child have back in thailand.

He/She is thai national by birth so has full rights in Thailand. Just need to be registered in Thai system if not done already.

hey hey, just like me

Fairly simple, the child will be a Thai national and if one of the parents is also a permanent resident/Australian citizen, the child will be an Australian citizen also.

The Australian side will take care of itself, but from the Thai side, you will have to get a Thai birth certificate issued by the Thai embassy in Canberra. This I beleive can be done by post.

The Thai passport is also issued via the embassy in Canberra, and can be done once the birth cerificate is issued. It is a bit more of a pain however as it requires that the applicant be physcially present to get the electronic photograph and fingerprint taken. However, the embassy regularly sends a team down to each of the state capitals to so that passport applications can be taken. Check with the embassy to see when this happens next.