Adv maths doesnt require the departments approval (well not last year anyway). You'll be able to change your subjects from the 15th February. It'll appear on Myuni and student admin, and you can vary your subjects. You should be able to change to adv maths without any hassle. If not, go to orientation day and bring in your HSC results to the maths deprtment to prove you did go well in maths.
Considering you got a band 6 for both, you should be doing adv maths.
Considering you got a band 6 for both, you should be doing adv maths.