1 day a week for 3 months? I'm a nanny /babysitter and I would be very surprised. If you want to give her a nice card and maybe an extra bonus of $25 or $50 that would be thoughtful and generous but IMO completely unnecessary.
My last client that I parted ways from, after working with her when DS was 4 months old until he turned 3 and started preschool, for 3 days per week, didn't get me a gift, or give a bonus or severance. She gave me a heartfelt thank you note and a lovely letter of recommendation. Honestly, given how much time I'd spent with them I expected more, but for a one day a week job for three months a parting gift is a bit silly.