“There will be no fanum tax under a government I lead”. Either fanum actually means carbon, or more likely she just chose some random word that fit the metre of Gillard’s now-infamous line.

Fanum Tax is one I do actually know the origins of. There are a group of US streamers popular with Gen Alpha who live in a share house and they’ve developed a comedy bit during the streams of one of them, Kai Cenat, where he sits down to eat some food before his friend, Fanum, barges into the room and demands Kai give him the food. When this happens, everyone spams “fanum tax” in the chat. So in it’s original form it’s referring to food theft (the kind of thing kids do at school I guess). I don’t know if it’s evolved any further from that.

Anyway, as you suspected much of her speech was Alpha slang rather than Zoomer slang.