Is It Currently Possible To Travel To New Zealand From Australia Without A Pport?

No you need a pport. I think you may be confusing with applying for Australian Citizenship. If you are a a foreigner say British living in New Zealand, once you have lived in NZ for a set number of years (not sure how many) you can apply for citizenship of Australia which makes working and buying houses easier. Also you get better Medical cover. Best Google question or contact the relevant Embies for up to date info and relevancy to you nationality and cirstances.