1)You do realise if you went that route, that 'she, in her name' (not you) would have to bring the total purchase price in from overseas. Inward remittance would have to be in her name. You cannot use money already in Thailand.
2)Using her Australian passport to purchase is probably feasible, but at some stage (either at the Bank or the Land Office) someone is going to query the lack of Visa/Extension/entry stamps in her passport, then she will need to show her Thai ID and this may cause problems.
Be careful.