I lived in Aus for 7 years. Here are some downsides (but this was early noughties):
My husband was mocked incessantly for being British. Ok, some see it as banter, but it became tiresome. He’s pretty thick skinned too.
For me, I never felt I was really accepted. I lived in a major city, but not Sydney or Melbourne. I have lived as a foreigner in London and felt more welcome and at home. Many Aussies seem to mistrust, or at least not fully embrace, anyone with a different accent. Something in the culture was off.
Road rage. A major problem. So many angry drivers.
Rage in general. Aussies love giving someone a ‘telling off’.
Ants. You will never enjoy picnic without getting invaded.
Mosquitos. Sitting outside at night means wearing a shedload of repellent.
Getting honked at, leered at and shouted at by men in cars. That has never happened to me in the UK but was common in Australia.
Getting groped by men in clubs and bars. I realise it happens in the UK too, but was way more common in Australia.
The other things like snakes and spiders weren’t a huge deal for me.