Dog Control Act 1996
Yes, But you may need to obey laws to do with things like leashes, registration and dangerous dogs. There will be bylaws set by your local council that you can check. If you bring an animal you can be held responsible for its actions.
People from overseas get the same protections as
New Zealand residents during a protest
Even if you’re not a resident of New Zealand, you’re still allowed to protest, so long as you don’t break the law.
However if you are convicted of an offence this might affect your visa or ability to gain residency status later on. For information about being deported for criminal offending, see the chapter “Immigration”, under “Deportation: Being made to leave New Zealand”.