K.L.
If she is providing care out of her home and is licensed, she's not technically a nanny. The title "nanny" generally means that they come to your home.
Anyway, if she is licensed through the state it means that her home has been inspected and meets safety requirements, she has gone through training for multiple things - including CPR, first aid, SIDS, etc. It also means she and anyone living in her home have passed fingerprinting background check. You have the right to be able to view all of these documents! Don't hesitate to ask for references of families she has cared for in the past, as they can be a wonderful resource for you.
As for your baby, she will adjust. It may take a couple days, maybe even a couple weeks to be fully adjusted.
My son has been surrounded by distractions since the beginning. My almost 4 yr old niece adores him and I was working as a nanny (went back when he was 3 wks old and took him with me) until the mom stopped working and my position was eliminated. My son is 4 mos old and he can eat and sleep anywhere. Your daughter will learn to also.