Thanks, you speak English really well, too. Oh, it's your first language so I shouldn't be surprised? Well, it's my first language as well, so where's your surprise coming from? Yes, really. It is perfectly possible for people born outside Australia (or England, Canada, the US, wherever else your Zone of English Language Exclusion extends) to speak English as a first language. It's not the only language I speak but it is the one that I use the most and therefore am most fluent in. I do wish I spoke my other languages better, especially the ones my ancestors spoke, but seeing that that ball got dropped at least two generations back it's been a lot less accessible to us than English.
I might have accumulated a tiny bit of angst after several years of introducing myself to ignorant people. It's only in the past few years that I've stopped trying to explain myself, and still more recently that I've given up the overcompensating streak that I subconsciously applied to make up for any handicaps that others might have assumed I needed on the sole basis of where I was born.
By the way, it works both ways: there are elderly members of my family who, despite our best efforts to explain the diversity of the world's geography, cannot be persuaded that there indeed exist "red hairs" (direct translation from the Hokkien term for Caucasian) who don't speak a word of English. It's easy to assume things based on your narrow experience of people of a certain skin colour or birthplace. I just hope this awareness has adequately transferred into all areas of my life, not only language. I want to experience people and places at their best and truest, not through the distortions of my preconceptions.