A great deal of Australia is severely dry - think Arizona or New Mexico or parts of Texas. A great deal is very hot - ditto, or Florida, and points more tropical. A great deal of it is both. That's why so much of the population is around the coastline. Not all of the coastline either - a lot of coastline is desert - particularly around the Great Australian Bight (Nullarbor Plain), and on the west and nort-west coast of Western Australia. A lot of coastline is part of areas too tropical to be readily developed, so while it COULD be developed as heavily as Indonesia or the Phillipines, it hasn't been.
As someone said, they aren't giving land away though. It's tied up - either owned by large pastoral companies (including King Ranch from USA, and Vesteys from UK). A lot is public reserve, and will stay that way - they're buying back leasehold and freehold to add to the public land. And a lot is native people's reserves, which they manage as they see fit - often as pastoral areas.
For broad sweep and details about Australia check the World FactBook your CIA maintains - great resource -
http://www.cia.gov/cia/publications/factbook/
Note that immigration, as people said, is NOT easy. Australia provides a great deal for its residents. For instance, we have a national Medicare system which pays for (or at least reimburses) most medical costs. Free (taxpayer-funded) health care for residents is a right. There are other social welfare benefits as well. They don't let freeloaders in easily.
For information about immigration see
http://www.immi.gov.au/
If you have a LOT of money you can come in. If you are sponsored by an employer you can get in, provided the job couldn't be readily filled by an Australian. This is easier in regional Australia (which you would be interested in), rather than capital cities. The major category to which this would apply is medical practitioners or nurses. If either you or your spouse are nurses or doctors qualified in the USA, UK, Canada or NZ then you're pretty well home free. Other places - check it out - qualifications may need to be upgraded. Another area is teachers - particularly science or maths teachers. This is tricky - some of the public school systems (by state) require a local certification in addition to professional degrees. However, private schools aren't so fussy/unrealistic/union dominated, and if you had any sort of a job you would be able to study the local certification by distance education (correspondence and the web).
If you want a serious winter, choose Tasmania or parts of Victoria or New South Wales around the Snowy Mountains, or New South Wales around the New England Ranges, or EXTREMELY limited high areas of Queensland around Stanthorpe. Some people also say the Atherton Tablelands in Queensland, but I just don't believe it.
If you don't like freezing your little buns off, don't go there. There's a lot of tropical Australia that could be much more developed than it is, There's a lot of inland Australia which could be more intensively farmed, on a smaller scale, than it is. Dry country, and you need to learn to handle it, but I love it. There's very little land within reach of the coast which is still available and affordable. Strangely, some which is, heavily timbered, coastal, good rainfall, is around Eden. That's a town on the south coast of New South Wales. Near but not in the Snowy Mountains. Definite winter, but not to the extent that your buns would shatter if someone hit them with a stick.
For anyone from the USA used to the attitudes towards firearms ingrained by the rights in your constitution - get over it. You can still have firearms, but there are definite limitations. Shooters must be licenced, their firearms must be registered, they must be stored safely (specific gun-safe requirements by law), and they are subject to inspection. That said, I don't personally know anyone whose firearms have been inspected, although it does happen. The attitude towards firarms is that they are tools or sporting goods. They are NOT for defence (except for the defence forces). You cannot own a self-loading rifle, or a self-loading or pump-action shotgun (exceptions on VERY expensive licences for professional shooters or farmers for pest control). You cannot own a pistol of calibre greater than .380 (except .44/.45 single-action for Western Action shooters). In fact, pistols are generally for target-shooting use, not for hunting. Fair enough - we don't have bears or cougars - you generally have time to pick up a long arm for anything that needs shooting.
Note that you can use a special pistol calibre 45/38 which is a necked-down .45ACP. Perfectly legal, if you're licenced. Changed top and barrel on a 1911A. I don't believe everyone who had a .45ACP and is now running a 45/38 actually turned in the .45 parts, although of course if they were to run the old pieces from time to time they'd be limited to casting their own bullets (or running some strange lever-action rifle which happened to feed .45ACP cartridges).
If you understood that to say shotguns are limited to single or double barrel, you're right, but aren't they all? Almost all are single-shot or side-by-side or under-and-over. However, Australia is making a reproduction of a 189x Winchester lever-action shotgun, and bolt-action is also allowable.
