Uh oh, did someone call the lawyers? I'll try to keep this brief and concise...
1. Everything hinges around what's written in the contract. Unless it's an employment contract, you have no legal recourse to back pay etc, nor does it have to be registered anywhere.
2. It's very likely that you may be owed superannuation. In simple terms, companies have an obligation to pay super to contractors who are contracted wholly and principally for labour.
3. Don't confuse contractor/employee legal tests for tax purposes with those for contract or employment law purposes. They may not be cross considered, and courts (rightly or wrongly) have distinctly different tests for each. Just because you're considered an employee by the ATO, does not mean that you're considered an employee for employment or contract law purposes.
On the balance of probability, I'd say it's likely that you dug a hole for yourself when you signed a contract for the provision of service, rather than one for employment. Why did you think the terms were agreeable then but not now?
Some things for you to consider...
a) Do you hold Workers Comp Insurance?
b) Do you hold public liability or professional indemnity insurance?
c) Do you charge by the hour or by the flight?
d) Do you use your own charts, uniforms, nav equipment etc?
e) Are you free to nominate someone else to fill the contract duties (ie could you send another pilot in your place without question)?
f) Do you invoice the company, or do you fill a timesheet?
These are the types of things a court will consider when deciding if you're an employee.
If you want some help, PM me your contract. I'd be happy to look it over.
Seriously though, put this one down to experience and find a better job with a reputable employer. Your's sounds like gutter trash to me.
BTW - The following is for free;
"Contractors generally have their own insurance."
That's one part of it you should be very concerned about, not just the low pay. If you kill or injure someone, or yourself, or break an aircraft, who's paying?
If you're a 'contractor' and don't have appropriate insurance, you could be in trouble. Get some professional advice.
The charter company has a bunch of common law responsibilities that they can't contract out of. That is, they have a responsibility to ensure the safe passage of their fares or hirers.
If you hurt someone while you're flying on their behalf, you're nicely insulated from any liability to their pax.
Watch out for this however... if the charter company is sued they could then in turn sue you for your negligence, which caused the accident (and their subsequent financial loss). My tip to you though is that if you're uninsured, the court will probably decide you're not liable because you're an employee, and they'll scratch around collecting all sorts of evidence to prop up their judgement. Courts generally don't like to find against parties that can't afford to pay in negligence actions.
The charter company's deep pocketed insurer is a much more attractive target to the charter company's lawyers than little 'ol broke pilot.
If such a legal action mounts, you should buy some popcorn, sit on the sideline and be ready to be entertained by everyone's lawyers (including the charter company) suddenly and madly scrambling to prove that you are, and always were, an employee!