Just because you are earning below the national average doesn't mean you are worth paying average or more, you have said that you are paid around the standard rate for the work, which is determined by the job market or floors set in associated awards or EBAs.
Comparing your income to the national average is not a good way to evaluate your rate of pay anyway, you need to compare it to what others are earning in comparable roles at comparable companies. This is easy to find online from salary surveys, just looking at Seek now it's saying 75-80k for sous chef. If you are under that then that's the kind of evidence you should be taking to your meeting. If you think you are better than average then you need to justify what value you are bringing that makes you more valuable than the average.
Your employer will know what the averages are, if it is a big company they usually have access to services that provide them with all this info.
In my experience businesses will always prioritise bottom-line over loyalty, employees should do the same. We go to work to trade our time for as much remuneration as we can, people who are loyal to an employer are usually taken advantage of.
I'm a software engineer and I usually ask for pay rises after 12 months. I make a case, if the rise I'm looking for is forthcoming great, if not I immediately start searching for a new job. When I get a higher offer I take it and don't consider any counter offer from my current employer even if it is higher because staying never works out in the long run.