This is a new species to me.
It
looks a little like our brush cherry.
I did find the following:
http://farrer.csu.edu.au/ASGAP/s-aus.html
"S.australe is a hardy tree in most temperate and subtropical climates and is cultivated in most Australian states. It prefers rich soils and assured moisture"
They sell some of this genus over at bonsai palace
http://www.bonsaipalace.net.au/page18.htm
In general, the most common mistakes are keeping hardy trees indoors (they need sunshine and ventilation) and over/underwatering.
Getting it outdoors may do it some real good.
Another common problem is that many commercial trees are underpotted, or just small enough that watering can be tricky. You want to be sure not to overwater, but you also need to water before the soil dries out. If that sounds complicated, it is. Usually a beginner will start with a plant that is pretty tolerant of watering mistakes. Elm is pretty good that way, as you can overwater it quite a bit and still keep the tree.