No, these state estimated taxes were withheld from your nanny's wages when you submitted the payments to Virginia on VA-5, whether that was monthly or quarterly. The state withholdings would have been reported on your nanny's W-2 statement when you (or your payroll company) prepared that form. The state estimated tax payments would not impact your personal state income tax return.
Please see Household Employer Withholding Tax (nanny tax) for more details.
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