The 500Fs superceded the 500D in 1965 - don't know what happened to the 500E, maybe that was a Mercedes designation

- with the most obvious external difference being the conversion from rear hinged 'suicide' doors to safer front hinged doors.
As far as I know the 500F ran until about 1972, joined by the 500L from 1968. Both were replaced by the 500R in 1972.
The 500Fs had the 'whisker' front badge like yours with the early cars having a rear 'Nuova 500' badge.
When the 500L was introduced, the rear badge was changed to one that said 'Fiat 500' like yours. So I guess yours dates between 1968 and 1972.
The VIN will give you a hint. It's located on the right-hand side (as you look at it with the bonnet open) of the firewall in the front compartment. Yours should say 'FIAT 110F*xxxxxxx* where the x's are the sequential body/chassis production number starting from 110F*0000001* in 1965. About 2,272,000 F's and L's poured off the production lines in Turin, so your chassis number will give you a rough idea of when your car was made. You may also be able to find out when it was first registered in Australia.
Hope this helps,
Chris
PS: You can also email Fiat and ask - I did this and never heard back from them. Shame really because other Italian car companies (eg: Alfa & Ferrari) keep really good records that are available to the public.
PPS: It looks like a really nice little car.