If you refer to general circulation Australian Pennies rather than Proof coins, the order runs something like this -
1. 1930 Penny is the rarest
2. 1920 Penny with no dots on the reverse
3. 1925 Penny
4. 1946 Penny
The rarest Australian coin minted for general circulation would be the 1930 Penny of which there were only 3,000 minted. It is currently esitmated that there are still about 1,500 of these still being traded in the market.
1909
A 1909-S VDB penny!
The rarest British Penny would be the 1954 Penny. There is one known to exist, maybe two, but there could be some doubt about the second.
The rarest and most valuable Lincoln cent that isn't an error is the 1909-S with VDB on it. The rarest and most valuable error Lincoln cent is the 1943 copper penny.
Indian head penny
The last Australian Penny was minted in 1964.
Indian head penny
The last Australian Penny was minted in 1964.
The last Australian Penny was minted in 1964.
The last Australian Penny was minted in 1964.
Only the Philadelphia mint made pennies in 1900. There isn't really a rarest.