To be honest, you could probably get by doing any subjects you want in High School. [Look below for explanation]
Well, if you want to go to University in Sydney, you're going to have to wait a bit - no university in Sydney offers Dentistry undergraduate. You'll have to do it postgraduate (which means doing it -after- you finish a first degree, like Science, Medical Science, Arts, Commerce etc). Because you can pretty much get into Dentistry from any Bachelor degree, therefore it doesn't really matter what subjects you do in Yr 11/12.
USyd does offer Dentistry postgrad, not sure about UNSW and other Sydney universities.
I'm not 100% sure, but orthodontics probably requires specialisation in Dentistry, sooooooo yeah, so that's probably another year on top of Dentistry degree.
So since you're in Year 10 now, it will take another 2.5 years to finish HSC. If you want to go to University in Sydney, you'll have to do a Bachelor's degree, which will take you 3 years, Dentistry will take you another 4 years, Orthodontics is probably specialisation so another 1 year.
So from now? 10.5 years? Good times ahead for you.
If you're willing to travel outside Sydney, Charles Sturt University and La Trobe offer Dentistry undergraduate for 5 years. Means you'll probably get your degree in 8.5 years from now. But CSU and La Trobe are literally in the middle of nowhere (Orange and Bendigo respectively).