Speaking from my experience having a nanny for my 4 kids, I can tell you that a week is not enough time to find out if your child will bond with your nanny. It IS enough time though for you to observe her with your child and gauge whether or not you feel comfortable with your choice and are willing to let her continue to care for your child. I’m assuming of course this observation time is the last step in your selection process, and that she’s otherwise well qualified, has good references, and is compatible with your parenting style.
Now that you have had the chance to see her in action, you should let her do her job. My kids always behave differently around me and their dad. Even if we are just in the background, not involved, our mere presence changes the dynamic between them and each other (not a concern for your only child) and them and whoever was taking care of them, whether it be their nanny or a relative, or a teacher.
It’s important for you to consider that your child must form a bond with the nanny. Some people find this hard to accept, and others don’t expect it, but it’s one of the main advantages (amongst others!) to choosing a nanny over a child care facility. A nanny will provide personalized, one on one, full time care so of course a bond is formed. That being said, how long did it take you to bond with your child? It probably took more than a week for you and your baby to get into a routine, and then even longer to really REALLY connect. At 11 months, you are still getting to know each other!
An important question was raised in the comments: what does the nanny report? If the nanny feels there are/will be issues then that is cause for concern. However, if she is good at her job, she likely knows that it is too soon to tell if her and baby are a good fit. Especially since she hasn’t really been allowed to do it. If you are picking up the baby when he cries, you are not letting her be a source of comfort and care for your baby, which is what you are paying her to do.
To give you some insight into my experience, I had a nanny for my 4 kids up until recently when grandparents took over. We hired her when my 2nd child was 6 months old and I returned to work full time. My oldest child was 6. It took her about 3 weeks to settle in. I went back in November, and by December my son was happy to go to her in the morning. My 3rd baby went into her full time care sooner-at 3 months. I did as you are doing; I had her start 3 weeks before my maternity leave ended. My 3rd baby was colicky and miserable. He cried constantly. Wouldn’t nap. She was very nervous about not being able to handle him, so I had her come while I was still home so she could build up the (emotional) stamina to take care of him plus my toddler. That first week, when we were home together, I thought she was gonna quit for sure. But, once I started work and they were on their own together-my nanny and the two little boys, plus my oldest, 8 by then, everything was fine. (To this day, my 3rd baby remains extremely attached to the nanny. He visits her often, while none of the other kids do.) In fact, it was like he was a different baby altogether with her. He saved all his crying and ill-temper for me when I got home. :-/
My daughter was the toughest for my nanny. I went back to work at 3 months, like with my third, and while she was pleasant and cheerful for me she was surly and demanding for the nanny. She was breastfed like the others but the only one who refused a bottle. I had to leave work 3 times the first week alone to feed her bc she wouldn’t eat, sleep, or stop crying. The second week was better, and then the third, and by 1 month she was chugging down 12-16 oz if expressed breastmilk in her bottles without hesitation. It did take her a solid 3 months however to smile when my nanny showed up in the morning, but by 6 months they were good friends. The important thing to note tho is that despite how difficult it was (for me, the nanny, my daughter) we stuck to the plan and it worked out. We made the right choice back in 2010, and it was proven again in 2012 and 2016.
What all of this means is that it’s not the nanny necessarily. It might be your baby. Not that there’s anything wrong with him! He might need time to learn to trust your nanny. If you trust your nanny, as I did, even though my kids clung to me and cried and begged me not to go at times, your baby will trust her, as mine trusted and eventually loved my nanny. But not after 1 week. Be patient.