If you are giving one month cash in lieu, you do not need to provide her a reason. Perhaps, you just say we do not need you now. This was what we did before.
When you fire her, you should prepare a letter stating your decision to terminate the contract with immediate effect by paying her one month in lieu; preparing a cash cheque with her name on it for the amount you pay her - (1) one month in lieu; (2) travel allowance of $100; (3) oustanding annual leave entitlement in lieu; (4) other outstanding wages you owe her... or (5) an agreed amount for the ticket back home.
I booked the ticket and ask her to pick up at the travel agent (written down on the letter as well).
Then, we packed everything and we changed the lock of the door. Done.