I had to obtain a permit in order to travel OS with the Whatnot Guitar as it has Brazilian Rosewood back and sides and I also had to get one to be able to send Nick in NZ the BRW Uke trim that he bought.
The people in the above mentioned section of the DSEWPaC (that's the official acronym) were a pleasure to deal with. The major problem with getting a permit is lack of documentation. I had documentation in the form of letters and photographs and a Statutory Declaration so it all went through with out a hitch.
So it is not a huge insurmountable obstacle but it takes a little bit of time and just getting your i's dotted and your t's crossed so that the law is satisfied.
Anyway I thought that I would post for the general education of everyone here as knowledge is power...

Cheers
John