I looked at this a few weeks ago (done nothing yet of course) and my builder brother suggested just sticking another layer on top of the existing plasterboard rather than ripping the wall open and stuffing it with batts.
But - this is the important bit - he also said it would be much, much better to use the products that are designed to cut the noise. The stuff's called Soundstop (Boral) or Soundchek (CSR Gyprock) and maybe there's some other versions.
It looks like normal plasterboard but it's heaps heavier and denser. Their respective web sites have the specs. If you want to get tricky you can batten it out so there's minimal contact between the layers - they have special fasteners for that.
I don't know how that compares with doing it the proper way with batts as well, but unless your neighbours are as noisy as mine it's probably no big deal.
You might have to order it in from your building materials supplier, after first having the guy behind the counter, who's stone deaf from listening to talkback radio at 250db for the past 40 years, sneer at you like you're an idiot for even asking.
This was my first post. It hardly hurt at all.