I fell like age one can be hard like this. My baby (1 year old) loves baby dolls, but even with that she still can move on quickly. I have also said this before, but I will say it again. I don't like a lot of clutter and I don't like a lot of toys that don't get played with.
When I give a gift I want it to be loved and used A LOT. This has been a struggle this year with my baby. Thankfully I am done Christmas shopping for her and I really do think the gifts that I got will be great. There is a wide range of different types of toys and activities and I think that will help keep things interesting for her.
I have also mentioned this before, but what to mention it again: Ever since I have had kids I have liked to have Santa bring them 4 gifts. Those include: something you want, something you need, something to wear, and something to read. I do also put 7 things in their stockings as well. Those include: something to read, something to play with, something to help you learn, something to help you create, something to eat, something to use, and something to wear.
This helps me come up with things that have meaning and also have a purpose. Those are two things that I want and that I want to teach my girls. I would love to share with you what I got for my daughter and hopefully it will help you come up with some ideas for a one year old in your life!