When you say "Silver", do you mean made of silver or, silver in appearance? Does the coin have a denomination marked on it? I can only find two Australian Coins with "eagles" on them and neither of them are dated 1983.
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With the possible exception of traders tokens (with the traders business name on them), there were no "Australian" coins minted prior to 1910.
There was a period from 1855 to 1870 during which Sovereigns and Half-Sovereigns were minted in Australia with the words "SYDNEY MINT" and "AUSTRALIA" on the reverse, but this was more a matter of convenience for the Royal Mint rather than the minting of an Australian currency, since Australia did not exist as a country until 1901.
Sovereigns and Half-Sovereigns were minted variously at the Melbourne, Perth and Sydney Mints until 1931, but these were minted on behalf of the Royal Mint and to the British pattern with no referrence to Australia on them, other than the mintmarks M, P and S.
An Australian 2001 gold 1oz nugget (One Hundred Dollars)(Elizabeth II), uncirculated and in absolute mint condition and the opriginal packaging, could fetch up to $1,350 AUD.
There were 150 minted.
A reputable coin dealer will be able to give a more accurate valuation.
Apart from the odd Proof or bullion coins issued in sets, Australia does not issue a "silver" Dollar coin. Australian One Dollar coins are made from a copper-aluminium-nickel alloy and have a "gold" appearance.
The Australian 1999 One Dollar coin was issued as a commemorative for the "International Year of Older Persons", such commemoratives being an occasional departure from the usual 5 kangaroos design.
The Australian 1999 One Dollar coin has the international logo for the "International Year of Older Persons" on the reverse.
There were no Australian Dollar coins, either commemorative or for general circulation, issued in the 1960's.
For a valuation to be given, the year of the coin would need to be known, and the theme.
Queen Elizabeth II is on the front of coins, not the back.