Do you have to go to a University in your country?

You can, although there are a few things to think about:

1- Going to university overseas costs a LOT of money. You can expect to fork out tens of thousands of dollars every semester for the privilege, and Australia's subsidy program for higher education won't pay for it, whereas in Australia they will. In Australia, you can go to university without paying fees up-front; the government covers them initially, and you pay it back as part of your taxes (if you have a university debt, you pay a few extra percent tax each year until it's paid off). This is why you rarely hear about people in Australia saving up for years to send their kids to college like you do in the USA.

2- Most Australian universities are actually very well-recognised around the world and their academic standards compare quite favourably to many others. They don't quite match up to say, Cambridge or Harvard, but they are at least as good as anything else (also, by no means does everyone in the USA go to a Harvard-tier university, I'll put it like that). I wouldn't immediately assume that going overseas will get you more opportunities than Australia will unless you've seriously analysed different programs to reach that conclusion.

3- For some degrees, it doesn't matter where you go, but for some, it does. For example, something like an arts degree or whatever, it doesn't matter. Some degrees, though, have legal recognition for different professions, and that does matter (especially as these are the degrees you want if you want a job). So for instance, if you want to be, say, a doctor, you must have a medical degree that is recognised by the Medical Council of Australia, and some overseas degrees may not meet the required standard (also it is a very cumbersome process to get the credentials recognised in many cases). And it's not just medicine, many other degrees are like this in Australia.

Basically, I'd seriously think about whether or not this is the right move. I wouldn't make a decision like this based on "oh, some of the universities don't seem that great".

You don't have to you could go anywhere, but you won't get government funding or loans, you have to cover the cost yourself, both fees and living expenses. If you want to go overseas you will need to look at what the options are and the expense. One thing to consider is that degrees in the UK generally only take three years, not four, (except medicine) so that would lessen the cost.

You could also consider moving within Australia. I know most Australian students continue living with their parents throughout university, which would limit your options, but you could look further afield within Australia and get accommodation. Obviously that adds expense compared to living with your parents but it would be cheaper than studying overseas.

There are some good, well respected universities in Australia, in the major cities.

There is also the question of what you want to study, because not all universities are evenly good across all subjects. You need to research where is good for whatever it is you want to study.

You can study anywhere in the world; provided you meet the requirements to do so.

To get a student visa, you generally need:
- proven fluency in the language of the country
- a confirmed full time university place
- proof you can afford the full cost of living and studying there

There are a million foreign students in the US alone! Of course you can go to university abroad IF:
1. you meet requirements for admission to the university. They each set their own requirements.
2. you & your parents have the money for all school + living expenses, plus return transportation to your country of citizenship for your degree/program.

Do your homework! You have a lot of research to do to select a university - and plan to get into a highly rated school for your intended field of study since job competition is generally very tough pretty much everywhere on the planet.