Without a specific, notable version of this claim to address, we're just in the realm of speculation about what the meme actually means.
Here is a list of the world's deadliest animals, confirmed by two sources.
- Mosquito (all regions) (Also see Achille et al. 2010: "In terms of morbidity and mortality caused by vector-borne diseases, mosquitoes are the most dangerous animals confronting mankind", and Wilson 2007: "The most dangerous animals on Earth are in fact mosquitoes")
- Asian Cobra (Asia)
- Australian Box Jellyfish (Australia)
- Great White Shark (all regions)
- African Lion (Africa)
- Crocodile (Americas, Africa, Asia, Australia)
- Elephant (Africa, Asia) (See Henja et al. 2012: "elephants are among the world's most dangerous
- Polar Bear (North America, Asia)
- Cape Buffalo (Africa)
- Poison Dart Frog (Central/South America)
Of these 10, counting roughly, there 4 are present in Australia, 6 are present in Africa, 4 in South America, 4 in North America, 6 in Asia, 2 in Europe.
The most dangerous species in the world are not more present in Australia than elsewhere.
To properly answer the question "Is australian fauna more dangerous?", we'd need:
- a ranking of all fauna by dangerousness
- the list of fauna in Australia
- the list of fauna elsewhere in the world
Then, we could compare the average dangerousness rank of Australian fauna vs the average rank of fauna elsewhere in the world.
Achille, G. N., Christophe, H. S., & Yilian, L. (2010). Effect of Bacillus thuringiensis var. israelensis (H-14) on Culex, Aedes and Anopheles larvae (Cotonou; Benin). Stem Cell, 1(1), 60-8.
Wilson, R. I. (2007). Neurobiology: Scent secrets of insects. Nature, 445(7123), 30-31.
Hejna, P., Zátopková, L., & Šafr, M. (2012). A fatal elephant attack. Journal of forensic sciences, 57(1), 267-269.