Frequency/market practice: Stamp duty is not payable on share transfers (provided that the target company does not directly or indirectly hold significant interests in land, i.e., is not a "landholder"). Where landholder duty applies to a share transfer, the liability at law is usually borne by the buyer, although some Australian jurisdictions (at law) impose joint and several liability on the buyer and the target company itself.
Stamp duty on asset transfers is usually borne by the buyer (at law in most Australian states/territories) and it is highly unusual for parties to agree otherwise. The rate varies between asset types and between states.
Broadly, parties are free to contractually allocate the economic burden of any duty that applies to a particular transaction as they wish, but this does not abrogate or modify the liability that is imposed under legislation.