I wouldn't go to too much expense. It can be a bit awkward when you're staying with someone and they spend lots of money on you but you're on a backpacker's budget.

Her own set of keys.
A sim card
Some toiletries
An Australian version of her preferred bevvy
Some vegemite (if you don't tell her it's food you can amuse yourself while she tries to figure out what the hell it is)
A map of Australia