Jay,
As someone who has B.Sc with a Zoology Major, I would strongly recommend anyone that has an interest in wildlife and science - and is accepted into uni - to do something similar. The work is very different to school, and if you do a Science degree (or an Arts degree with lots of science subjects) you should come out at the the end thinking like a scientist. This can be beneficial in your work later in life (example: I currently work as a foods inspector - nothing to do with zoology - and I've used the knowledge I gained at uni to analyse data statistically and predict trends and volumes of imports, and last week did some mathematical modelling in relation to our sampling/testing regime. Impressed myself because until then the only modelling I had done was the Starship Enterprise about 15 years ago).
The TAFE Certificate in Zookeeping is not essential for working in the field. If you are employed by Taronga and haven't done the course, you'll be employed on the understanding that you will commence it the next year. Speak to ARP management and see if they think it worthwhile doing it. When I did it some years ago the ARP students were a little miffed it was concentrating almost entirely on Taronga, and had only a small reptile component. If you are interested in things other than herps and plan to be a zookeeper then this course would be very worthwhile.
Once you have your Cetificate in Zookeeping or a Uni degree, there are three courses offered by Charles Sturt Uni as distance subjects: the Graduate Certificate, Graduate Diploma and Master of Vertebrate Management. I haven't done these courses but friends from Taronga have and say it is pretty good. The Masters course has 'Captive Reptilian Management' as one of the final year courses
http://www.csu.edu.au/courses/pg/sci/gd_cvm/
The ASZK website has a list of zoo keeper related courses at
http://www.aszk.org.au/Links - Keeper Training & Education.htm
If you're interested in working in a zoo or wildlife park then, as Basketcase has already said, volunteering is very important as hands-on experience cannot be taught. It also gives the facility a chance to see you in action.
Hix