My 2 cents worth.....
I am a CPEng and currently working for a European car manufacturer here in Melbourne - this is despite my original degree being in Electrical Engineering!! My advice would be to consider a couple of things:
1. Consider getting some hands-on experience with work straight out of school - there is no rush to get your degree. If I am hiring for an engineering/technical position then I will generally pick someone with some real-life experience over somebody who just has an engineering degree. I have also found that guys/girls who have spent some time "on the tools" are generally more effective engineers as they are better able to consider the practical aspects of design (if you have had to swear, curse, and skin knuckles to get access to a bolt head to undo it then you are more likely to consider maintainability and accessibility when you are designing something as an engineer.
2. Consider getting a haircut and joining the Army/Navy/Air Force
This is worth serious consideration as there aren't many other employers that I know of that will pay you to study!! I joined the Army as an Apprentice at the age of 17 back in 1989. After 2 years of study and another year of On The Job Training I was a qualified Electronics Technician and worked in various roles for the next 7 years as a soldier. I had done yr 12 before joining up (not a pre-req for the Apprentice Scheme) and this allowed me to apply for and be accepted to become an Army Officer and study Electrical Engineering at ADFA (UNSW). I got paid a full wage to study full-time for four years (Defence also paid my HECS fees) and then after graduating I was posted to Defence's project organisation (Defence Materiel Organisation) in Melbourne where I worked in a number of projects (mostly with armoured vehicles). While I was there, I also completed a Masters in Project Management (distance learning through ADFA (UNSW) and paid for by Defence) and eventually got out of the Army after 18 years and did a couple of Government jobs before moving to my current employer. During my 18 years I spent 6 years in full time study, one year of On The Job Training, with at least another 12 months spent in full time training courses (including a 2 month physical trainers course, several promotion courses, and specific equipment courses)........I don't know of any other employers who will invest this much in their personnel!!!
Unfortunately the Apprentice scheme doesn't exist anymore but it might be worth you checking out the ADFA website or perhaps speaking with your local Defence Recruiting Centre (please note that I no longer work for Defence and I won't get a finders fee if you sign up!!).
I would also agree with one of the previous comments about joining Engineers Australia - I am pretty sure that they offer free student memberships and they have some good resources that you could use to educate yourself about the engineering profession in general. I was similar to you at your age in that I loved maths and physics and fortunately for me I was pretty good at them too which helped a lot when I eventually did my degree. I find it a little bit ironic/amusing that you get right into the maths/physics side of things when you are at uni but once you are out in the real world then you are really utilising critical thinking and an analytical mindset more than the maths and physics that you learnt in uni (at least this has been the case in the roles that I have been in - I have not used Laplace Transforms, Fourier Transforms, or Quantum Mechanics since finishing my degree!!).
Mech Eng would be a great base for you and there are plenty of fields that this could lead to. The automotive industry opportunities in Australia are shrinking at the moment but there is a lot out there in other industries including rail, mining, and defence and the field of Systems Safety is also growing rapidly at the moment.
Good luck with whatever path you choose to follow!!
Cheers,
Gags