Yes, the Local Government Act 1995 and other acts of Parliament give any local government the power to make a local law.

No. Local law making by local governments is subject to the authority of State Parliament and a dedicated Parliamentary committee that reviews all local laws made by local governments. If a local law made by a local government is beyond lawful power or does not have an Act of Parliament to enable it, the Parliamentary committee can recommend to Parliament it be struck out. 

It is a requirement of the Local Government Act 1995 to do so.

As the local environmental health enforcement agency, the City needs a regulatory mechanism to deal with nuisance issues that can arise from time to time in the district involving odour, noise, dust, vermin control, hoarding and pollution complaints. The proposed local law continues the mechanism that has existed for many years in the district and will repeal the existing Animals and Nuisance Local Law, and the Bee Keeping Local Law with a single contemporary local law.