This is the information on the official SES website regarding using BBq's in local parks;
Can I have a BBQ in my local park?
Yes. But only under strict conditions. There must be a dedicated area set aside by the state authority or local government responsible for the park. You can only use an electric appliance or gas appliance that has an enclosed flame. All flammable material must be cleared five metres around the appliance. Short green grass less than five centimetres in height, paving stones, bricks and reticulated gardens are not considered to be flammable. You cannot burn solid fuels such as wood or charcoal in the open air.