In Australia, animals tend to be the domain of coins, but there are a few examples of animals on backnotes.
Pre decimal 10 pound, George V & George VI issues. Signature series looks like Coombs/Watts so most likely late 1940's/early 1950's
$1 - 1966-1984 Aboriginal artwork
$2 - 1966-1988 John Macarthur and marino sheep
Current $10 & $100 note, both featuring horses.