Weed or Not a Weed?

Coming from England, I don't really know much about Australian plants except if it's a native, you're probably ok to stick it in your garden. Having it's own unique eco-system over here means that if you plant the right things it encourages the right insects and wildlife and you don't accidentally wipe out a species of butterfly or tempt a family of cane toads to take up residence in your water-feature. It would all be so easy if I could tell by looking which was a weed or a non-native. 
This one's not a weed, by the way. It is a nice well-behaved substitute for an Umbrella Tree... which is a naughty weed.