If you give your maid a month notice, then the answer is yes, you don't have to pay for the one month notice payment. However, you will still need to pay for the single trip ticket and the proportional annual holiday that she entitles to during her contract.
From what I have seen so far, the one month notice only works for those employer and maid remaining in good terms. If she is not up to your satisfaction, you better off to pay her and get rid of her immediately without further fussy and complications