It is not against the law to do your own conveyancing work. However, conveyancing work is highly technical and highly specialised. Do not attempt to do your own conveyancing unless you know precisely what to do and are certain you have the capacity to do it before you enter into the transaction. You cannot expect any assistance from the conveyancer acting for other party. If you make an error, you may cause settlement to be delayed (causing default interest to be payable by you) or even enable the other party to terminate the contract.
If you are considering doing the conveyancing work yourself, look at the list of tasks to be undertaken by a conveyancer and tick off those that you are experienced in doing.
Interestingly, very few real estate agents attempt to do their own conveyancing when buying or selling for themselves.
Please note that NSW is in the process of adopting electronic conveyancing, this will become mandatory in mid 2018 and has substantial implications for the conveyancing process.