Having finished high school last year, and wanting to be a zookeeper myself, I took the initiative to go to university rather than TAFE. I am currently studying Animal Science which opens up a lot more opportunities than a diploma at TAFE does as, if you don't know already, zookeeping is a really competitive field. A degree at uni can open up opportunities in National Parks and Wildlife, lab work, field research, environmental planning, teaching and so on.
In saying that, after I graduate, I will probably go straight to TAFE to complete Certificate 2 + 3 in Captive Animals. I actually contacted a number of zoos in Aus and they recommended TAFE, especially Taronga Zoo which has a specialised TAFE facility. In other words, a uni degree (for me) is not only a back-up to go to other fields of work, but also gives you more qualifications that put you above the rest.
The actual most important thing (in my opinion, and directly from the mouth of the zoos I contacted) is that you start to gain volunteering experience. Start now if you can volunteering at zoos, wildlife parks, vets, etc. so you gain that hands on experience which can lead to job opportunities opening up.
Hope that helps somewhat
