In theory Melbourne has Catt IIIB available on 16, though I don't have a set of NOTAMs with me right now, so I don't know if it's currently available. There wasn't an issue last time I flew there.
But, it's not just the airfield that you have to worry about. Plonking a decent ILS (or GLS) installation onto an airfield only means that it will be available to those aircraft and pilots qualified to use it, and even then the minima can differ from aircraft to aircraft. For instance, the visibility requirement for QF's 330/380 is less than that required for the 767/747...and on my charts the 737s are not even listed. There are extensive ongoing training requirements, and it is quite conceivable that an airline could do the maths and decide that they are not cost effective.
Take off is also effected, with vis requirements that are longer than needed to land (because landings and rollout are automatic, whereas take off is not, and you also have to consider the engine failure scenario). Beyond that, it slows everything dramatically, so even if the airport is operating, taxiing around takes forever, and then, of course, the queues build up.
I would move heaven and earth to go up the night before. If fog is present, you can pretty much kiss any connection goodbye.
