Zero interest for AUD fixed deposit, RM recommend to invest in AUD Unit Trust: JP Morgan Investment Funds - Global Income Fund. What should I do with my AUD? Exchange back to SGD? Invest the AUD?

The only reason why you want to keep a foreign currency is due to having some sort of ties to that country. AKA, family, or home. Keeping a currency due to hope that the currency performs better is foolish, your RM cannot predict the future of the currency, neither can you. If you have no ties to Australia, and if you intend to continue living in Singapore for the longer term, you will be better off just converting it back to SGD and using it to invest in other asset classes that reflect your financial objectives.

I guess it depends on the amount of AUD you have? If it is not very substantial, would suggest just converting back to SGD. Even if you invest in the AUD share class of the fund, eventually you would want to convert the AUD back to SGD to use. Alternatively, keep the AUD and invest in the fund and withdraw next time you go back to Australia (when travel is back).