I don't know of anyone using the Perone system, but judging by the information I found with a quick Google search, there are a few that have it working for them. Try one out and see how you go - as long as your hive complies with the relevant state regulations regarding frames etc you should be fine. There are people in Tasmania who advocate using 12 frame Langstroth full depth boxes/supers (whatever you want to call them!!!) that are square and can be fitted any way round - similar to some hives used in the UK and Ireland (like the Rose system) That would be similar to a Perone hive except for the 90 deg corners ...but gee those boxes must be heavy even empty. There are also Kenya top bar hives, long Langstroths etc that all have some advantages and some disadvantages. In Australia, generally you will have to make your own equipment unless you choose to use Langstroth hives (or possibly Warre hives). Beekeeping is pretty much a sea of compromises and just about every design of hive tries to take advantage of some aspect(s) of honey bees' natural behavior. At the end of the day, bees are pretty adaptable and are quite happy to live in all sorts of weird and wonderful places - around here they love house roof spaces and wall cavities, and they seem to be strong and healthy. Quite often bees will do exactly what they want regardless of how natural you try to make their environment.
Of course the ultimate size that a colony can become is dictated a bit by the space they have to occupy and also by the climate as the shorter growing seasons, the less time to build up and the more likelihood that they will need a more compact area to survive winter. One disadvantage of a big strong Perone colony, or a Langstroth one for that matter, is that they might get slightly defensive (or actively hunt you down :whip:). Fun if you have the right protective gear, but if they get inside your veil and give you a touch up on the eyebrows or on your nose (most likely both) you know that people are going to look at you funny when you walk down the street for the next few days. Also, sometimes you might be doing something unrelated to beekeeping a fair distance away and be completely unaware that you have just violated one of their laws that requires you or your kids to be punished. I'm not trying to scare you as most bees are generally pretty gentle most of the time, but if they have something substantial to protect they might surprise you.
Like I said, as long as everything is legal, and the DPI inspectors are usually pretty helpful with such queries, try one of two out. You will probably want at least two colonies so that if one gets into trouble, you have some spare resources to help them - that also relies on having removable frames so that your equipment can be swapped around. As a more widely known "natural" alternative, have a look at http://www.naturalbeekeeping.com.au/home.html
Whatever type of equipment you choose to settle on should be related to what you are trying to achieve - from maximum high volume honey production, queen rearing, pollination, interesting hobby with honey benefits to a living WBC hive garden ornament. As Prestonpaul said, everyone has an opinion (usually different) ...or are like me and have several differing opinions (Lone, that has nothing to do with coming from Tasmania :-P ).
Good luck Damian, beekeeping is very interesting and very addictive.