Council is not responsible for creeks and watercourses running through you property.
Council is only responsible where there are pits and pipes within your property and within an easement to Council. For information on titles please see:
Certificate of Title
All creeks and watercourses operate under common law and as the resident or land owner you are responsible for the maintenance and upkeep of the watercourse and to ensure the watercourse can take adequate flow without blockages and causing flooding to you or upstream.
If you are getting flooded by your creek or watercourse please ensure it has adequate capacity to take all flows and work with your adjoining land owner to ensure they have no blockages or flow restrictions.