You should be able to get a USD bank account in AU, then receive your payments from stripe without any conversion.
Stripe only pays out in the same currency of the country the account is setup in. Rumours are this is changing, if anyone from Stripe reads this and is looking for beta testers please get in touch (contact details in profile)
https://support.stripe.com/questions/which-currencies-does-s...
(we also use Paypal and a couple of other providers - spreading billing between multiple providers is a good thing)