There are many different key events in Australia's history that have helped shape our multicultural society.
^Is that your intro? If so, perhaps, you can elaborate... All you did was, quite frankly, repeat the question asked. Maybe you can start off introducing what multicultural society is and why it is important. You can also add how many countries have influences on each other to make the world it is today.
When it all began in 1949,
you may want to change that to: It all began in 1949 when there was a shortage...
there was a shortage of scientific and engineering skills and knowledge in Australia needed to complete the scheme
You should explain what the Scheme really is. I, not know what a Snowy Mountain Scheme is, have NO clue what the purpose to the scheme was.
A large international recruitment programme was carried out.
I'd add something like "To address this problem" or "To fix this issue". Something of that line to connect to the last sentence.
There were 100,000 people working on the scheme between 1949 and 1974,
Change it to: 100,000 people worked on the scheme between 1949...
Why is Scheme capitalized in some sentences while not in others?