If I become a citizen of New Zealand, can I apply for jobs or PR in Australia?

Yes, as a New Zealand citizen, you can move to Australia and work there without applying for a visa in advance. On arrival, you will receive a Special Category Visa (subclass 444), which lets you live, work, and study in Australia indefinitely.

This visa does not grant Australian permanent residency (PR) or citizenship. To obtain PR, you must go through Australia's standard immigration process. After living in Australia for at least four years on this visa, you may be eligible to apply directly for Australian citizenship without first getting PR.