Seems like that's way too cheap.

I am in Chicago and for a nanny typically you should expect to pay $2400 - $3200 a month depending on the hours per week.  Mine comes at 8am and leaves at 6pm, Monday through Friday.

You will need to check the following:

1. Immunization records: some basic shots or test results such as Hep A, B, C, etc.

2. First aid certification

3. Maybe ask her to do flu shot.  You should offer to pay for her shots if she has not had some of them

4. References from previous employers and their contact information.  You should contact some of them to inquiry about the performance of your nanny.