The Dog Control Act 1996 has a list of laws that it changes, which you can find in the part of the act called Enactments amended. You can see that the Dog Control Act 1996 is allowed to make these changes because of section 79.
The laws that are changed include the Animals Protection Act 1960, the Local Government Act 1974, the Ombudsmen Act 1975, the Privacy Act 1993, and the Summary Proceedings Act 1957.
When you look at the Enactments amended part of the Dog Control Act 1996, you will see the exact laws that are changed, which helps you understand what the act does.