If you just have 4-1/2 months to go, you do not have the need to terminate her by giving her 1 month $$.
I would wait till the end of the contract if I were you. You need 2-3 months to have the replacement in place. I would buy time and choose the most suitable one.
If I were you will waiting finish contract. Then no need to paid extra cost, at the same time call agent to find other one to replace. Normally find other helper need 2 -3 nmonths.