I live in Perth.
River Gum - not likely to be any good
Pine - dont bother
Our Box is not the same as Marc is talking about.
Never heared of Balar.
I have made a few bows from Mallee, and have had great results.
however, there is about 1000 species of mallee, but if it is straight and dense, should be good.
The ones I have used are 'fluted gimlett' and 'merritt'. sg about .9 and hard as tool steel. It is very good in tension, and resists compression. Not as brittle as the larger eucalypts, (i.e. euc. regans).
Keep the nocks small to reduce tip weight, and start with longer bows until you know the wood.
Good Luck - Mal