I'm not going to claim to know all the ins and outs of planning for diversions, but I know for a fact that CBR is used quite often during the winter for diversions from SYD due fog. CBR's now a primary diversion port for Korean, and it saw 747's, A340's and a 777 on the same day last winter.
There are facilities available for the 777 and 747 such as stairs, pushback tugs, etc. but I'm pretty certain they're managed by either Qantas or another contractor and would probably have to be charged to the airline.
Maybe give the port authority a call? I'm sure they'd be able to steer you in the right direction.