Congratulations on making the decision to get involved in the sport and a good first step would be to join the local SSAA
http://www.ssaawa.org.au/. SSAA membership should be sufficient to support your "Genuine Reason" for requiring a firearms license, and they should also be able to provide you a list of approved clubs and ranges. Another association is the NRA
https://www.nraa.com.au/associations-clubs/ and he link provides a list of clubs in Australia. SSAA / NRA is a bit like the Holden Vrs Ford debate in that both have their fans and detractors, check them both out and make an informed decision on which may suit your needs and beliefs best.
From 0 to 600yd in a single bound is probably a bit of a stretch for new starters for a couple of reasons. To actually achieve a degree of accuracy at that range will require the learning and understand of reloading ammunition and the added expense that entails. Not saying it can't be done but it's a lot to learn if you don't have a knowledgeable friend guiding you. The risk of jumping in the deep end is you may not get the results you expected or enjoy yourself which leads to disappointment. 600yds isn't a huge range but it's far enough that a degree of experience and skill is required along with knowing exactly what the rifle and you are capable of doing.
As with many members here, I started with an air rifle then a 22lr and worked progressively up the calibre ladder as I gained experience and learnt. Buy yourself a good quality 22LR that doesn't break the bank and 10,000 rounds. Hit the range to practise and practise and practise some more till you can consistently hit a 10c coin at 50m. When you can repeat that at 100m look at maybe buying a .223 to get the hang of centre fire and learn how to develop an accurate load by reloading your own ammunition. This exercise will quite likely cost you less in the long run and be more educational along with building some valuable experience. I have everything from .177 air rifle up to 50BMG in the safe and shoot to >1500m but I still hit the 50m range on a regular basis with the .22lr to practise cause if I can't hit a 10c coin at 50m then I'm no chance of hitting a rabbit at 600 plus it's cheap and still a heap of fun. Something to think about in economic terms, 22lr is around 7c a shot, .223 is 79c a shot for Federal 50gr factory rounds and the bigger stuff can cost up to $12 a shot...I know which round I prefer to learn with.
Welcome aboard
Brett