The policy move is an effort to stop heavy boozers (the targeteed group is probably aborigines) from drinking themselves silly on cheap flagon wine. In a sense it is an imperfect surrogate for volumetric pricing - for pricing alcoholic drinks on the basis of their alcohol content not their value. This policy identifies ethyl alcohol content as the prime cause of alcohol’s social costs and advises taxing in accord with the ethyl alcohol content. Unlike a tax a minimum price would give revenue to booze companies not the government. 

A minimum price would force a switch towards drinking better quality booze with price at or above the minimum away from booze currently priced below the minimum. There would also be a reduction in overall consumption.  The Chateau Cardboard aborigines, if they did drink, would move upmarket.

The measure would have regressive impacts as PM Brown notes and will undoubtedly be criticized in Australia on these grounds. This, in itself, is a poor argument because regressivity should be assessed from the viewpoint of the total impact of  tax-transfer mixes, not the impact of a particular tax.

Minimum prices might restrain limited income youth from experimenting with booze which is a good thing.

Minimum prices might foster the creation of homemade brews with health and other costs.  It might, for example, encourage substitution toward non-alcoholic intoxicants such as petrol sniffing and smoking cannabis.

Minimum prices would reduce problem drinking by those with drinking problems though the precise effects are a matter of evidence. Dependent drinkers might be income-constrained but their compensated price elasticities are low.

The standard microeconomics argument here is that setting minimum prices provides deadweight losses in the sense that consumers lose more than booze sellers can possibly gain.  This is correct if their are no externalities associated with alcohol consumption (bashing up wives, raping adolescent kids, killing others in cars)  and if their are no internalities asociated with flawed judgements in relation to drinking.