Your result
Australia — Marriage
Not eligible
A partner visa needs a sponsor, and the sponsor has to be an Australian citizen, an Australian permanent resident, or an eligible New Zealand citizen. On what you have described your partner is none of those, so there is nobody who can sponsor the application and this route is closed for now.
It is closed rather than impossible, and it turns entirely on your partner's status rather than on yours. If your partner is working towards permanent residence themselves, the partner visa becomes available to you the moment they get it — so their application is effectively also yours, and it is the thing worth concentrating on. If they are a New Zealand citizen, whether they can sponsor depends on the kind of visa they hold and how long they have been in Australia, which is worth checking rather than assuming, because the answer is sometimes yes.
If neither of you has a route through the other, you are both in the ordinary migration system. Points-tested skilled migration and employer sponsorship are assessed on occupation, age, English and work experience, and a couple can generally be included in a single application, with one of you as the primary applicant and the other as a dependent — so it is worth working out which of you scores better before either applies.