· Unless Jane is under 30 she cannot get a working holiday visa (immigration.govt.nz/Work/ United+Kingdom+Citizens+Working+Holiday+Scheme.htm). NZ Immigration is not interested in any previous working holidays in Australia (unless you have been deported or committed a criminal offence there) - Australian immigration policy is nothing to do with ours.

It's reasonably difficult to get a general work permit in NZ. You need to have either an in-demand occupation (there is a formal list) or an offer of employment from an NZ company who has applied to the immigration department to recruit overseas: (immigration. govt.nz/Work/General+Work+Policy.htm). However, there is some leeway if you just want to do part-time work, but I'm not too sure how generous that leeway may be.
Tracy MacShane