The best info about the route, including possible camping spots, is by the NZ Department of Conservation:Ball Pass Crossing
And the Ball Pass route
page here on Summitpost is pretty good too.
Rock climbing experience is not necessary, but you'll need good route finding skills and the ability to self arrest on steep ice or snow or you may find yourself in serious trouble.
Route finding is already a bit tricky in bright sunshine, and a lot more so in poor visibility. If you take a wrong turn somewhere, you may have to retrace your steps, or even camp unplanned until you can see something again. With enough spare food that shouldn't be too much of a problem, although in really stormy weather camping near Ball Pass is best avoided.Ball Pass from the Hooker side
As to the ice and snow section, the part of the route on the glacier on the Hooker valley side below Ball Pass is potentially dangerous. Nothing in Australia compares to this. If you fall in the wrong place on ice, it's steep enough to be potentially deadly, and it's hard to self arrest on ice. If there is no trail to follow, avoid the steepest parts by going high early when you reach the glacier from the Hooker side and then traverse high on the glacier to the saddle.
However, if the glacier has a nice layer of snow on top, it's a lot safer, as self arrest would be a whole lot easier then (but if you don't know how to do that, get some instruction first, or go with a guide). You can get the latest info about the route conditions and weather forecast in Mount Cook village.
P.S. I've done the route guided, with the company that owns Caroline Hut.The Caroline Face of Aoraki / Mount Cook