Caltrop, sometimes referred to as Bindi-eye or Double gee, is common in the coastal areas of across northern Australia. Some people regard it as native to Australia, others say it is native to Europe, probably the Mediterranean region. Although a native plant, it is considered a weed by some because of its spiny 
fruit. Whereever it comes from, it really hurts when you get those sharp burrs stuck in your foot!
Caltrop is declared as a noxious weed in the NT and as prohibited entrants in WA! They also puncture bicycle tyres, dog’s paws and stock hooves and have even been reported to be toxic to sheep.
Society for Kimberley Indigenous Plants and Animals 
Your confusing a number of different species here, some native to WA and some not.
Caltrop is the main offender, its proper name is Tribulus terrestris and it is a Pest Plant in a number of shires and this species is not native to Australia.
The common name bindi-eye, or bindi usually refers to Soliva sessilis its not native
Doublegee is the common name for Emex australis and not a native
There are no Prohibited Tribulus species under WA Biosecurity Legislation.
There are over a dozen native Tribulus species across WA, Florabase has a list if your interested.
cheers,