I am going to Australia to study for a Master's. I am an electrical engineer and I am thinking about taking my tools like a soldering station, screw drivers, etc along but I wonder if it will be allowed on a plane. I will be carrying one big suitcase for everything and a small backpack for minor items. Should I keep that soldering station in the big suitcase? Should I take it along?
Put it in the checked bag and you should be fine, assuming it's a conventional mains-powered soldering station. There is no reason to bring it into the cabin (they're not fragile, valuable or useful in-flight) so just don't do it. Some overzealous person might think you'll stick in a sharp point and stab someone or plug it into your in-seat power and proceed to employ thermal-rectal cryptanalysis techniques. Personal experience- I had bringing on on-board questioned (but not prohibited, but it hung on opinion) even before 9/11, and things have tightened up infinitely since then.
Of course butane or battery-powered soldering irons are entirely another matter.
I have, on occasion, had sharp-looking tools (regardless of whether they were actually sharp) taken off me at security. If you're checking a bag, put it in your checked bag. If you're not, at least unscrew the tip from the iron, so it looks less stabby.
I'm not aware of any country with travel restrictions that'd prevent you from taking a soldering station in a checked bag.
As others have said, these belong in checked baggage, not in-cabin.
You might want to prepare for questions at customs about your intent. One aspect would be: are these occupational tools, and do you intend to seek enmployment here? Another might be, are these bomb-making tools? Either way, I'd be prepared to convince them that you'll be using these things strictly in a harmless hobby or educational role.
Depending on how much stuff you are taking/how long you are spending in Australia, it might make more sense to box your equipment and other personal items that you won't need while travelling and ship them to your destination. This might then allow you to get by with one carry-on item which is more convenient for airline terminal transfers, buses/cabs, or any amount of walking. Also, if you happen to be booked on an airline that charges for checked-in bags, shipping your stuff might make financial sense as well.