Cash for her college fund...wrap it up in a box because from all her gifts she will like the boxes and wrapping paper the most!
I'm usually not one to recommend savings bond for adults, but it can be a great gift for a kid - she may not appreciate it now..but when it matures she will be old enough to appreciate it. Her parents will appreciate it too.
when my niece turned 1 i bought her a bunch of the Mr. Men series books that my sister (her mom) and I used to love as kids. my sister loved the gift and was happy to be able to read those books to her daughter and continue the tradition. look for something your sibling (assuming it is a sibling's kid) liked a lot as a kid and can pass down to this child.
A one year old will be interested in something for five minutes and entertained by it and then it will be tossed aside never to be used again. Tell her about a dream of yours when you were a kid, like maybe a desire to climb mt everst or something. She will be entertained by it for five minutes and never think of it again juat like how most of us treat our dreams.
Leapfrog makes an awesome line of toys for newborns up to 6 years of age. Go to a Toys R Us, find their row, and pick something that looks fun. Their toys are pretty accurately labeled for the appropriate age. The Tag Jr. is a great item for little ones, but she probably wouldn't use it until she was 18 months. That might make a great Christmas gift.
Don't know what your budget is, but my nephew got this when he was 1 and it's been passed down to my kids. They've all loved it... Step 2 Up & Down Roller Coaster About $105 new. Probably can find them used, too.
