As the other poster says, New Year is not a gift-giving season. A gift might be given, if you're visiting the homes of your superior in your company, elders in the extended family, customers, etc., but they are always only small "token" gifts, never expensive--like a small box of green tea or a bottle of good Japanese sake or wine.
If you need it to be of good value to express your appreciation of the person, why not called it a "belated" Christmas gift. If she knows Western customs, I'm sure she'll be delighted. I'd appreciate any "belated" Christmas gift!
Just my two cents!