Currently my baby sitter is a family friend who is a SAHM so just paying her to have the girls. Just like someone might have a friend babysit their kids when they go out for the night. So its baby sitting not nannying
i'm looking at trying to do the same thing again - babysitting rather than nannying in which case i would then have to be do the tax thing etc.
Only problem is that once she earns a certain amount, it can effect her benefits etc. This is one extremely fine line with regards to tax etc that I'd never want to cross, because all you need is for somebody to dob you and your babysitter into ato/centrelink/whoever you both could get in trouble.

Also written agreements are a contract, which implys a working arrangement.

I'd still be getting public liability insurance for your place if that is where the girls will be looked after, or at least asking your potential babysitter to get it if your children are staying there.