Museum
I'm going to confess to getting this story wrong initially and I'm delighted that renowned composer and PM of the Hawthorn City Pipe Band, Mr. Mark Saul, recently stepped forward to clarify things. I had confused the bagpipe pictured to the right with the images below. 

The bagpipe (pictured to the right) was featured in the Piping Times, Vol 33 no. 2, November 1980.  Mr. Tom Anderson of Brisbane was the owner at the time. He wrote that they were made by John Center in the Grassmarket, Edinburgh workshop around 1880 for an industrial exhibition in the city.

The silver is hand-chased and aside from hand-carving and engraving, the bores of all the drones and slides were reported to be lined with silver. The blow pipe has a copper tube running through it to prevent cracking. The chanter sole was said to be solid silver, 3 1/2 inches wide and 1/4 inches thick.
 
I had confused the bagpipe in the Piping Times article with the images below. Mark was the photographer of the bagpipe below (in 2007) and was able to provide the following information.

The pipes in the old black and white photo from the Piping Times is not the same Center bagpipe! If you look closely you will see that the pipes in the black and white photo have strange large "lumps" at the top of the tuning chambers,
(I've updated the picture above and pointed to the "lumps" that Mark is referring to.) whereas the pipes in my photos do not. I have been told that they were a set of two specially made pipes for a World's fair. Strange that both sets ended up in Australia! The pipes are surprisingly light, probably because the mounts are not solid and neither is the chanter sole.

Mark, thank you so much for the incredible pictures and for bringing this information to the fore.

You can read more about Mark and his accomplishments/adventures at www.marksaul.com
The Bagpipe Place