He was described as being of Pacific Islander or Māori appearance, with a medium build and a black beard.
They are also after the driver of a white SUV seen outside the bank after the alleged heist, along with the driver of a dark Ford Territory spotted around the storage facility at the time of the theft.
The stolen goods were being sold online for about A$10 ($11) each, despite having a face value of A$1.
They differed from a set of three Bluey-themed coloured coins the Mint offered collectors in June.
Those 90,000 coins, which also have a face value of A$1, are being sold online for A$20.
One unfortunate collector had 189 of the stolen gold coins confiscated after purchasing them for about $1.50 each.
Bluey has become a global phenomenon after first airing in Australia on the ABC in 2018.
It follows the adventures of a young dog and her family living in suburban Brisbane.