The QDO said they were inspired to establish the campaign following a recent viral video from Kyogle dairy farmer Shane Hickey in which he outlined his struggles.
"Shane hit the nail on the head with his first viral video," QDO president Brian Tessmann said in a statement.
"People now get just how underpaid our farmers are and have shown that they want to do something to help."
The petitions calls on Coles and Woolworths to collect the levy by increasing prices and for milk processors to guarantee to pass the full amount back to farmers.
Both supermarkets quoted an ACCC report following an inquiry into the dairy sector, released in May, which found there was no link between prices paid to farmers by processors and the amount charged for private label milk in their stores.
"We believe a holistic solution involving industry and government is needed to drive meaningful and long-term reform in the dairy sector," a Woolworths spokesperson said in a statement.
The company says it has raised more than $7 million for Rural Aid to assist farmers, while Coles said it had contributed almost $11 million in donations, grants and interest-free loans to farmers and rural communities affected by drought.
Mr Tessmann backed the increase, saying grain prices had doubled, and hay in NSW and QLD was almost not securable even as prices had gone up "astronomically".
"We are hoping to give it a few weeks and then go back to the supermarkets, they are the key to it. There is really no excuse for them not to listen," Mr Tessmann told Melbourne's 3AW radio on Tuesday.