Need Craft Gift Idea for One-Year-Old Girl?

A yarn octopus would be fun. Use soft cotton or a styrofoam ball for the head, and cover with yarn, and then braid the 8 legs.

How about a fleece blankie. No sew-buy a length of fleece at the fabric store, fringe the edges, or buy 2 contrasting pieces, put them back to back, fringe and tie corresponding fringes together for a double thick fringed blanket. There are also lots of really cute printed panels that you can use to make cute stuffed animals, wall-hangings, etc. for her.

How about a homemade book. Use a photo album from the dollar store or ziploc baggies stapled together at one end and covered with tape. You can do an alphabet book with magazine pictures for every letter, a counting book, or even a book of relatives if you have family photos.

Many years ago someone gave me a bread dough picture frame with my child's picture in it. I still treasure it some 15 years later.
The whole thing is probably 3.5 inches in diameter.

I made this "Craft" for my one year old neice, You go to the fabric store and buy 1 patternd piece of fleece mesuring 1 1/2 yards, then you buy a matching solid color mesuring 1 1/2 yards. You need a large work space (clean floor works best.) You need a ruler and scisors (large pair) You lay the fabric on top of each other and cut 1inch wide slits along the blanket.

Or...make a sock puppet! Just make sure that everything is sewed on securely. Wouldn't want little fingers to pop little google eyes into little mouth.

Let the one year old be the "crafty" one! I've had lots of success making craft buckets for kids. Get a lidded plastic container (with a handle is best) and fill it with art supplies: big crayons, pad of paper, finger paint, washable markers, glue stick, stickers...