Hi Tashe.
Sorry if I sound a little harsh, but I'm talking as a result of my experiences. I said the same thing to one of my tuition students and steered her away from a biology degree.
To put it bluntly, I would not recommend any degree with the word "bio" in it. Australia does not do much cutting edge research in biology or medicine. I know 2 guys with PhDs in biology/medicine are they are not employed in medical research due to the lack of jobs. There are local jobs in biomedical engineering but far fewer than the number of graduates. Most of those jobs are in the USA and some countries in the EU.
Back when I finished high school, I was passionate about scientific research and improving the world. I watched numerous science documentaries and was mesmerised.
I did some medical research for my work experience, and for part of an honours thesis (I later quit this and started with a new supervisor). Reality did hit me, there are many cons to research despite the importance and prestige.
1. In the short term, there aren't many jobs in medical research, especially with government funding cuts
2. Research requires patience: a lot of reading of academic journals, a lot of failed experiments, a few dead end projects before you actually make a breakthrough.
3. Serious research roles above research assistant require PhDs (that's 4 years of tedious study).
4. Researchers are typically underpaid and overworked (60 hours per week shouldn't surprise you).
If research is your passion, go for it; otherwise, be practical and get a job with a profitable company. Your work might be mundane, but at least you'll have a decent salary and some time for family and friends. In the end, family and friends make you happy; a research project with a 20% success rate and negligible chance of a Nobel Prize does the opposite.
Should I do a science degree?
If you're doing mathematics or physics as a major, you're analytical skills will be useful for financial or risk analysis roles. Jobs in pure mathematics or physics are rare. There may be other good majors but biology and chemistry won't help much with getting a job unless you want to become a teacher.
Should I do an engineering degree?
If you have a knack for the technical things, yes. But focus on the foundation degrees like electrical, mechanical, mechatronics, software and civil. Nothing too specific (like naval or bioinformatics), because you'll be boxing yourself in when it comes to job seeking.
It's often better to talk to graduates and existing students, as some academics may spin a lot of BS to sell you the degree, hope this helps. I learnt the hard way, but in the end I found teaching. Best of luck with your choices, I hope they work out for you.