As far as general circulation coins are concerned, easily the most valuable Australian Penny is the 1930 Penny and the most valuable Halfpenny would be the 1923 Halfpenny.
The Australian Penny was issued in most years from 1911 to 1964 inclusive. Depending on their condition, the year they were minted, where they were minted, and any peculiarities of the coin, they could be worth anything from 50 cents to thousands of Dollars.
Most coin dealers should be able to sell you a 1936 Australian Penny.
Australian people value education and family the most
Australia did not strike any halfpennies until 1911, so the coin you're referring to is most likely English.
1877
Please ask one question at a time in the format "What is the value of a 1919 Australian Threepence" for example. Most answers already exist on WA.
Mathew Hayden
Most sell for about 25 cents.
Please see related answers
With the possible exception of traders tokens (with the traders business name on them), there were no "Australian" pennies minted prior to 1911. The only Pennies circulating in Australia prior to 1911 were British Pennies.
Such a coin does not exist. Australia was not discovered until 1770. Australian Pennies were minted in most years from 1911 to 1964 inclusive.