World Animal Protection, who started the petition, has said that breeding the animals in captivity goes against the main point of conservation.
When dolphins are bred in captivity, they aren't able to then be released into the wild as they're unable to survive on their own.
Ben Pearson, senior campaign manager for World Animal Protection, told 9News he doesn't believe that anything about Sea World's programme is helpful for the conservation of the species.
"There's nothing about this that is about conservation," he said.
"If they rescued a dolphin in the wild and they rehabilitated it, then put it in the wild, they'd have our support, but breeding in captivity is not doing that."
Credit: World Animal Protection/Dean Sewell
Pearson claims that the organisation is not intending to harm Sea World, or the economy of the Queensland area, but just want the company to stop needlessly breeding and keeping the species in captivity.
He explained: "A dolphin in captivity can live 50 years. In the wild, a bottlenose would swim 100 kilometres a day, it can dive 450 metres.
"They have a rich marine environment. There is no way a small concrete pool in Sea World can in any way replicate that."
The pools dolphins are kept in. Credit: Instagram/@seaworldaus
He went on to say that Sea World should start viewing its business as a sea sanctuary, rescuing endangered or injured animals and not just using captive ones for profit.
Sea World have defended its breeding programme, with a spokesperson saying: "While we are aware that some people do not support the idea of animals in human care, we are proud of our passionate team, our world-class facilities and our position as a global community leader in conservation and education."
The company has also received a boost in support from the Queensland government, as Minister for Agriculture and Fisheries Mark Furner commented: "Sea World currently holds an Exhibition Licence under the Exhibited Animals Act 2015.
"Sea World is approved to hold a maximum number of dolphins and is permitted to breed providing they do not exceed the maximum numbers allowed."
World Animal Protection's petition reached nearly 6,000 signatures in its first day, but it wasn't confirmed at what stage it would be presented to the local government.
Mr Pearson added: "We're hoping the Queensland Government will come very quickly, in which case we'll top the petition. If they refuse to do that, we'll leave the petition up for as long as we can and then present it to them."
Featured Image Credit: World Animal Protection/Dean Sewell