There is a 14" Celestron at Uni, but right now it's not usable as far as I know. I have an 8" Meade and there is another 10" Meade in town. Not much by the way of goto's of a decent size up here as not many peeps can afford one!!!. Apart from mine, the other one and the Uni, I don't think there's too many up here!!. What I could do is give you the email address of the Centre and they might be able to arrange something.
Here it is....
Astronomy@jcu.edu.au
Pass that onto the person in question and they can go from there.
You could also ring the Director of the Centre for Astronomy, Dr Andrew Walsh, on this number... (International: +61 7 4781 6437) and speak to him directly.