Acquiring exclusive use of an area of common property requires a general meeting resolution and the bar is generally high. It varies between states and according to other criteria but it could require an unopposed resolution of a general meeting. I suggest that any resolution should detail what you are permitted to do on that area and responsibility for maintenance.
Having the strata plan redrawn so as to include this area within your lot is a different approach with a similarly high bar.
The construction you propose would require both approval from the owners corporation and the local council.
I suggest you will need to do quite a bit of research and possibly seek professional legal advice before proceeding with a proposal.