Oh my!! I remember those days so fondly--both the trying to figure out what to get and upon realizing how easy it is, getting those things and enjoying life with my 1 year olds!
Anyway, it really is easy. Something to think about would be kitchen utensils. Sounds too simple, huh? I went out and purchased wooden spoons of all kinds/sizes, plastic measuring cup sets, plastic measuring spoons, plastic ice cream scoop, and stuff like that. She loved it! Not only that, as the years have passed, and we added another child, the collection has grown and they both continue to play with it at ages 6 and 3!
Don't underestimate washable crayons and a pad of paper/coloring book. Let her imagination lead her, don't really give her direction.
Another great gift at that age was this mid-sized plastic dump truck. Again, both girls still play with it through their travels.
My mom bought them a leap frog story-telling device. I know people who have sworn by them, but my kids were never interested--and the older daughter is a true bookworm in every sense at this point.
Both of our kids love their Weebles and treehouse and still play with them. By having a number of weebles, you can together create stories/scenarios and let your child lead.
Anything that she can manipulate with her hands is really your best bet. She is at an age where she wants to create--anything that you can get to help encourage that will be a winner.
Good luck to you! And, congratulations on *your* first birthday!