This fountain was commissioned for Melbourne's International Exhibition of 1880. It was designed and built by Josef Hochgurtel.
The International Exhibitions had the intention of drawing exhibits from the "civilised world" of Great Britain and Europe. The Australian component of the exhibition would then tour overseas to fly the Australian flag, or would have done had we had one at that time. The exhibitions had an importance which is hard to recall in the days of instant communications via the Internet or one day flights to any part of the globe via Boeing.
The fountain has the traditional European allegorical figures but also includes uniquely Australian elements; note, for example, the platypuses looking down from the second basin. (They're possibly a bit hard to see in this image which has by necessity been reduced to fit in a web browser (depending on your screen size), even if you view the image using the Original size setting.)
Even harder to see are the relief panels on the underside of that bowl; these display the four areas of knowledge on display at the exhibition. The arts, the sciences, commerce and trade, and industry (represented by, for example, reliefs of steam engines.)