The cost of your nanny is a nondeductible personal expense.
You can use amounts paid to the nanny to qualify for the child care credit.
@RobertG - the question was specifically about premiums paid toward the nanny's health insurance rather than wages. My understanding is that these should be deductible but it's not clear where this deduction should be taken.
@interti You will enter the amount paid for your nanny in schedule H for household employees. Then you will add any amounts paid for their health care to the amount paid to her and enter that into the amount paid for the child and dependent care credit.