Permanent low paid job to Fixed term high paid

Hi all, I'm working in a government department in New Zealand for the past 2 years since finished my PhD from Europe. I am holding a permanent senior analyst role but my pay doesn't match my position and getting paid 10K less than others in a similar role due to my lack of experience (if you count the years of experience) but I competed with others with experience when I got this role, and I am very productive and better than most at my level. My manager wasn't sure if I was good enough when offered me the position so she put me in a lower salary range than what I was supposed to get for my position. Now she apologised for that after seeing my performance and tried to increase to normal range but failed twice in past two financial years due to a tight budget so I lost hope. I like my job but low paid (so lower savings), and I don't have super stress at work and can spend quality time with family very well. I have a family with a toddler, have no financial liabilities except paying rent on time and buy food etc. and at the end of the month, I can save $1000. But it will take years to save for a deposit for buying a house here.

I'm about to get a 3-yr fixed-term job offer in Australia at a University (one step lower than my current position level at NZ, Senior Analyst to Analyst ) and I would love to work there for years but currently, they have the only 3-yr position as an analyst. The research centre at the University just opened recently will pay me about $30k extra per year than what I'm getting now in NZ and my living expenses will be similar so my savings will be doubled ($2000/month), which might help me save a deposit for a house there quickly. I feel there might be slightly more work stress than my current position but I don’t think it will be a huge issue. I have a feeling that I will be able to extend my position for few more years there and may be able to find a longer-term position after that in the same organization or somewhere else in the same city.

So, I’m in a dilemma and finding difficulties to make a decision - whether I should leave the permanent position to get a fixed-term position for better pay? Would love to hear your advice?