I have both US and Australian PPLs, and having flown VFR in both countries, there are some real differences in the VFR charts and supplemental data available. Mostly the contents are fairly evident but if you are unfamiliar with a specific type of VFR chart, it is important to look over the chart in detail to make sure you understand it.
The US publishes VFR charts known as Sectionals. These cover the entire country, including non-continental areas like Hawaii. IMHO these are excellent although in busy airspace, the 1:500,000 scale can become complex. So pilots learning to fly in the US usually become familiar with the sectional covering their base field, and then with that understanding, can look at sectionals for anywhere else in the US.
Printed sectionals can also be used for long range VFR flight planning as they can be laid out in sequence and routes plotted across adjoining chart boundaries. For online chart examination, SkyVector publishes all US sectionals online, which is a great resource.
Australia does not publish sectionals covering the whole country. It's a good question as to why but essentially the centre of the country is a big desert where few people live. So from a historical perspective, the inner part of the country has been regarded as "remote" and thus less in need of highly detailed maps. In addition, the word 'sectional' isn't even in Australian pilot lexicon, so use the word 'chart' instead.
Australia publishes Visual Terminal Charts (VTC) for each large metropolitan area which are a Mercator projection at 1:250,000. And there are Visual Navigational Charts (VNC) which mostly encapsulate the VTCs and are at 1:500,000 (same as sectionals). The image below is an example of the Brisbane VTC.
As VTC/VNCs cover only largely populated areas, for printed chart long VFR route planning, you will need to revert to the World Aeronautical Charts (WACs), pronounced 'whacks'.
WACs started as an ICAO project after WW2 to transition from the existing US-based international wartime series and so all Allied nations were effectively asked to harmonize their maps with a US design. But in 2015, the FAA stopped WAC production and thus a recently US-trained VFR PPL would never have heard of them(!)
The US WAC coverage looked like this:
WACs are a Lambert projection at 1:1,000,000 and in Australia, printed chart VFR route planning would be done over sequential WAC's, with likely a supplemental VNC chart for the populated areas to be crossed. WAC's do not contain airspace (although supposedly an aeronautical chart!). They are essentially a topo map with features that are easy to spot from the air.
So, to answer the OP's question - no, there are no free online sources for Australian government produced charts. SkyVector shows a very data sparse US Sectional-like view of Australia but I wouldn't use it for anything other than simple distance/leg planning.
However, all of the previously mentioned chart types for Australia are now encapsulated and adjoined in a single app known as OzRunways. I have no association with them, other than being a customer. Another answer has also referred to this as well.
OzRunways works on both iOS and Android and in my experience seems very widely used amongst Australian VFR pilots. For VFR use, they provide a so-called 'Hybrid VFR Map' which simply uses the most detailed chart available. Price at time of writing is about AUD $100 and chart-wise also has New Zealand and Papua New Guinea.
But also of value to pilots flying in Australia, there is comprehensive airfield information available in the ERSA (EnRoute Supplement Australia), which is a free download. It lists technical aspects/refueling contacts/etc. for every sizeable airfield in Australia. In addition to this, AOPA also publish a pilot guide for various airfields. OzRunways contains the ERSA and for an extra amount, they also will bundle the pilot's guide.
I would value any other comments about VFR chart sources for Australia but hopefully this is a good overview.