if she said she quit, you don't need to pay her one month salary. On the contrary, she need to pay you 1 month salary if she want to leave immediately or she need to give you 1 month notice. If she give you 1-month notice, and you want her to go immediately, you can discuss with her if it's ok if you let her go now, but she doesn't need to pay you 1-month salary.
My last helper is like that, she work for 28 days, and then she said she quit, she gave me 1-month notice, but i don't want to see her, so i let her go on the date she quit, and she doesn't need to pay me 1-month salary, but i still need to buy her the ticket.