Yes and no - it's not illegal to drive a bit under the speed limit, but if you drive abnormally slowly then you could be committing an offence.
Even though you're likely to gain the ire of any drivers behind you, you might sometimes want to drive under the speed limit when you're having trouble navigating a new area or waiting for a car park to miraculously appear at a peak time. Whatever your reasoning, remember that driving a bit under the speed limit is legally fine, but driving excessively slowly can actually land you in a bit of hot water.
According to the Royal Automobile Association, if you're driving excessively slowly you could be in breach of Australian Road Rule 125, which states that drivers must not unreasonably obstruct the path of another vehicle.
This isn't directly related to driving slowly but the rule does cover driving so slowly that you're obstructing others. There's some wriggle room as to how this law is applied but a clear cut example for all states in Australia, given by the RAA (and seconded by the New South Wales Roads and Maritime Services website), is driving 20 km/h in an 80 km/h zone. Driving that slowly would clearly be considered abnormal.
Although Australian Road Rules are nationwide, there tends to be a bit of variability between states in the nuances of certain road rules, their applications and their associated penalties - and context is often key as well. For example, the Western Australia Police Force state that there's a minimum speed limit on freeways in particular; you must drive no slower than 20 km/h under the designated speed limit on freeways, or you risk getting pulled over.
In general though, in all states and territories of Australia, you're best to just use common sense, as that's what police will be using when they see you driving on the road. When asked about driving under the speed limit for Tasmania's Daily Mercury a few years ago, Sergeant Lyndsay Judson was quite clear: "If I am out driving and come up behind you and you are travelling well under the speed limit and other vehicles are stuck behind you, then you can expect to be stopped and spoken to."
And finally, always remember that if you're driving in breach of the law you're probably also driving in breach of any insurance agreement you may have in place. While you should always check your specific agreement for details, be aware that if you get into an accident while driving so slowly that you cause an obstruction to other drivers, your insurance coverage could be voided.
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.