Here's a link to a good site on these insects. Case moth makes more sense as a name, I don't know why we called them casement moths when I was a kid . It's clear they are not just native to Australia, but the one in Grace's picture looks very like the ones I find everywhere I go at the right time of year.
If you can get hold of an empty case to play with you'll find the moth's silk is very tough, almost like silk and elastane in texture. Quite pleasant to touch.
Psychidae is a most elegant name for this moth family, and I shall use it for them from now on.