Christmas gifts for one year olds?
Diapers. Board books. Puzzles with a few big pieces. Coloring book & big crayons. Nerf toys. Soft dolls. Bath toys. Pop up tunnel to crawl through. Glow in the dark stars to stick to the bedroom ceiling, a nice picture for the bedroom, a mobile, a soft cozy blanket or quilt. Clothes, socks and shoes.
Your time + adventure: trip to the park, zoo, little playground, baby pool—indoor or outdoor as dictated by the weather, ice cream parlor, indoor soft play zone, baby swim class with you.
Do they still make finger paints? Stamps on paper or vegetable prints: (you) carve shapes out of carrots, potatoes, and cut an onion in half. Both of you paint the bottoms and stamp on paper. Frame your masterworks.
If you hate the parents get noisy toys like toy police cars with sirens, kid-sized musical instruments like drums, cymbals or horns, messy stuff like Smud, Slime, Pla-Doh or markers, hard toys to throw at your head, or a puppy. 
Paper towel roll , cardboard box , empty plastic water bottles , mix matches Tupperware lol 
just kidding but really my kids played with that stuff more then toys haha. Anything with flashy lights and sounds or a ride on car
Kitchen play set / ball pin / a little ride on with her favorite cartoon character/ a doll with a stroller .