AFAIK there are no cadetships for economics (where you work FT and study PT for some years and the reverse in others). UNSW might have a co-op program for economics which is sort've similar but you work with different companies each placement - check it out.
Internships - there are heaps, from the RBA where you will be doing true econ work to banks and financial institutions where forecasting interest rates, exchange rates, analysing global marcoeconomics etc will be your task(s).
Since most high level/practical economic work usually involves some kind of quantitative analysis, I suggest pairing your studies with a statistics degree - there will be plenty of stats in your econ major anyway, may as well have a piece of paper that says you're good at statistics too.