As the daughter has already paid you and you have no issue with her I would call up QF & divide the booking so the daughter can still travel as she's paid you for her ticket. You wouldn't want to be in the position where you looked like the bad guy because the daughter has paid you $2000.00 & you'd cancelled her ticket as well.
As the mother's pnr is now different to the daughter, call up QF reservations & make it a restricted booking & put a password on it eg "restricted booking/absolutely no changes/refunds to be made by passenger/any changes to booking must be made by (your name) quoting password". This would stop the mother ringing up and changing the date etc.
Quite a few companies put restrictions on bookings for their employees if they don't want them fiddling with them so they can keep track of who's going where.
IMHO you need to make it a cut and dried situation between yourself and the mother & the fact she hasn't paid you $2,000.00 for the ticket you have booked and paid for. If she's still in the booking with the daughter it makes it more complex that one has paid and one hasn't & that you've received partial monies which could be misconstrued as both of them having paid you $1,000.00.
Get a paper trail happening & issue an official looking receipt made out to the daughter stating that you have received payment in full from the daughter for her airfare only so you have it in black and white what the money is for and for whom.
You would now have a separate booking for the mother so issue an invoice for the outstanding full amount of her ticket then I would do one of two things depending on how close the impending date of departure is.
a) if you have several weeks before the date of departure & their is sufficient time to proceed with a claim through the small claims tribunal as mentioned in DK4's post leave the booking as is & find out from QF the last possible date you can ring up and cancel the flight (to avoid forfeiting the entire value of the ticket) so you know the deadline for putting the booking into a credit shell to be used for further travel.
b) if the travel date is in the very near future I would notify her in writing if you do not receive full monies eg 7 days prior to travel she will forfeit the booking but still be liable for the outstanding amount. Then put the booking into credit but still pursue her through the small claims tribunal then if and when she pays you she could then be given access to the credit shell to rebook when she's ready to travel.
Make sure you clarify with QF when the credit has to be used by & when all travel has to be completed eg she may have until 01 Mar 2013 to avail the credit however the travel may be for 01 Sep 2013.