This forum or any forum for that matter cannot give financial advice. Suggest talking to someone. If uncomfortable with financial advice, try doing your own research. First up you need to understand your risk tolerance. The fact you are in a fixed deposit indicates you have a low risk view. There are on line risk assessment you can do which may help.
Next suggest reseaching, hybrid shares, ETFs, LICs and REITs to find something that suits your risk appetite
I invest in the hybrid shares, LICs and ETFs as well as shares directly, but find as I am in retirement and looking at leisure time, the desire to have direct shares is reducing.
My holdings include ANZPG for hybrid shares, IVV, VEU, for ETFs, PL8, WAM for LICs, WPR, AVN, for Reits
AFI and ARG are also worth reviewing for LICs, VAS, IOZ, for ETFs, and VAP is a reit based ETF
The big four banks give good return and include franking credits, but whether this helps depends on you own financial position.
Many financial institutions will give you a free up front discussion for about an hour to outline options and the cost of their services. Based on your own statement, you are getting nothing out of the fixed deposit so some money invested in financial advice or your own research makes sense. Buy some books and the AFR and read it back to front regularly, talk to friends etc who are more investment savvy to give their experience.
There is a gap in Australia for financial advice and many seem to be biased towards their own products, which getting you to do your own research makes sense.
But as I always tell my son, you need to be able to sleep at night with the investments you make. And understand the fees attached which you do seem aware of.
Iggy