The Verdict: Not eligible
A partner visa is closed for now, because your partner is not an Australian citizen, permanent resident or eligible New Zealand citizen. Look at skilled migration, applying together as a couple.
Only those three can sponsor a partner, so it turns on your partner's status, not yours.
If your partner is working towards permanent residence, the partner visa opens to you the day they get it.
Until then, a couple can usually apply together for a skilled visa, with one as the main applicant and the other included. Work out which of you scores better on occupation, age, English and experience before either applies.