Hi there. I live in Coomera and I am a registered breeder with a Gold Coast Council permit. You apply to the council (I think the gentleman that handles this is called Norton). He comes out and inspects your property, records, food preparation area, dog accommodation, fences etc. You are subject to further inspections and the permit is not permanent. I think it is for three years and all dogs must be registered with the council.
This information is correct as far as I know, but best to check with the people in charge.
It was not a particularly onerous procedure and I was glad to be "legal" formally. If you have any other questions feel free to pm me :)
And, of course, welcome to Qld!