an increased demand for AUD will happen only if our exports are priced in AUD and are price inelastic - the price of the export will increase so if total outlay also increases, there will be more demand for AUD to pay for the exports, but most of our exports are price elastic anyway (and priced in USD)
Also, this completely ignores the reduction in the real interest rate with increased inflation, and the increased purchase of imports as they become cheaper relative to domestic goods.
So basically, false.
(as a response to the inflation rise monetary policy may be tightened which would increase investment and so on, but such effects are beyond the scope of the question - it's talking about right now).