Your nanny’s work is not related to your business so is not a business expense.
I assume you are talking about using the current partnership payroll system to pay the nanny so you don't need to get a personal EIN and file the quarterlies separately... can you do this ... yes you could HOWEVER you must keep excellent records for the 1065. It is not an expense for the partnership and NO PART OF IT cannot be deducted as expenses on the 1065 ... instead it must be listed as part of the partner's guaranteed payments.
This situation may be a focus of an audit so it is not the most correct way to handle it ... it would be better to keep it totally separate ... get a personal EIN to pay the quarterlies and issue the W-2. They are free and easy to get ... https://www.irs.gov/businesses/small-businesses-self-employed/how-to-apply-for-an-ein
with regard to your 1040, you would still be required to file Schedule H and there would be issues because any
payroll taxes would have to be paid under your 1040 SSN, not the LLC's EIN.
If you file payroll taxes using the 941 & 940 & whatever state form is needed annually then a Sch H is not required on the form 1040 ... using both methods means you pay the taxes twice.
This is more of a legal question but I agree with @Bsch4477
Your business can deduct ordinary and necessary expenses of running the business. Paying a nanny is a personal expense, not a business expense. So while you could maybe issue the checks in the name of the business and remit the employment taxes on the LLC's form 941, you can't deduct the nanny's salary as a business expense.
If it were me, I would keep things separate and pay the nanny from personal funds and report it on schedule H under your own SSN instead of the LLC EIN.