The easy answer here is no, it is not illegal to drive barefoot. However, as per many road rules in Australia a policeman can still fine you if they believe you are not in fully control of your vehicle.
While researching this article I actually tried to trace the etymology of the myth that it is illegal to drive barefoot, but was ultimately unsuccessful. I'll have to rack the mystery behind who was responsible for this old wife's tale to someone lost to the depths of the Internet, unfortunately.
Across Australia I have been unable to find any legislation explicitly forbidding driving barefoot or requiring you to cover your feet in some way. It is interesting to note that driving barefoot seems to be a uniquely Australian trait, despite us having hundreds of potentially deadly animals lurking by the sides of our roads.
The temptation is great, however, due to our hot climate and preference for wearing thongs (flip-flops for you Americans out there) to keep cool or for convenience after finishing at the beach.
Loose-fitting footwear like thongs (flip-flops) can easily be caught up underneath the pedals, causing people to lose control of their car with disastrous effect. This is why many driving instructors prefer people to drive barefoot over loose-fitting shoes, or even high-heels.
You do need to ensure you dry your feet and make sure they have solid grip of the pedals before setting off, however. It is also important to note some cars come with metal-finish on their pedals, which could scald the soles of your feet on extremely hot days when attempting to drive barefoot.
We also have not been able to find any reference to driving barefoot being an exclusion in comprehensive insurance policies, though we recommend checking the Product Disclosure Statement (PDS) for the full list of exclusions that apply to the product you have purchased.
Because it isn't strictly illegal to drive barefoot there is no law to quote, making this myth an easy one to propagate. But it's worth checking out this blog from a legal services provider, based in Sydney and operating nationally.
This article is not intended as legal advice. You should check with your local road authority to verify the information written here is suitable to your situation before driving in this manner.