There are definitions and tests to determine whether a person is an employee or a sub-contractor as far as the ATO is concerned. From what I understand there is a certain amount of flexibility about it, but basically a contractor will tend to use their own tools and do the same kind of work for more than one person or organisation. If your colleague fits these criteria and your accountant agrees, then there is no doubt that having her invoice you is much simpler for you than employing her, because you don't have to worry about withholding PAYG or Superannuation if she is a contractor. She'll need an ABN to invoice you, but they're easy and free.

I am not a fan of contracts and can't see any need for one here. Goodwill and generosity are much better business tools than contracts in my opinion.