This is a native species - possibly Long-nosed Dragon (Gowidon longirostris). The only basilisks that have been in Australian collections in recent times are Plumed Basilisks.
@WhistlingKite24 I was pretty iffy on the basilisk identification, thanks for the correction. Looking at pictures however, I am also doubtful of the Long-nosed Dragon identification.
@WhistlingKite24 Very useful list - wish I'd found it before. I haven't visited the facility for quite a few years even though it's only about a 20 minute drive from my place. Must do so when it opens again. They recently announced the death of their very old Lasiorhinus who they'd had for a long time.
It's a Lophognathus but I don't know which one (I find them confusing because the species are really variable, and the taxonomists are always changing which genera they are in!).
With @Goura ’s permission, I contacted Armadale Reptile Centre. They just got back to me and said it was a Gilbert’s Dragon (Amphibolurus/Lophognathus gilberti). Colloquially this species is sometimes called the ‘Ta-ta Lizard’ because it often does an arm-waving signal.
@WhistlingKite24 Oh good - in collections here it's labelled as 'long-nosed ta ta dragon' - it just didn't look like it had the 'long nose' that's so characteristic of the species. Could have been the angle of the photo