Christmas is always an awkward time if you have just started dating someone new. Do you but them a gift? Did they buy you a gift?
Basically, you don’t want to be in the situation of receiving a gift and not have one to give. And, likewise, you don’t want to give them a gift if they don’t have one for you.
This is an uncomfortable situation all the way around. So, it is best to have something just in case. Chances are that the woman will present her gift first. If she does, great. Then, you can present your gift. And, if she doesn’t present you with a gift, you can avoid the awkward situation by not presenting your gift to her.