My DD received this a few months after she turned one, for Hanukkah, but it has been one of her favorite toys for over a year now: the Baby Stella doll by Manhattan Toy. She's soft and cuddly and there are lots of accessories you can buy from a diaper bag with changing supplies, to outfits, to food. Add a $10 doll stroller -- maybe when your DD is a little older -- and you have little girl heaven!
Nora's loves popup books, her Little People train and farm sets.
Crayons and coloring books are also good - but get a very small box of big crayons. (her godparents - who don't have kids yet got her the 96 count of crayolas - yikes!)
Balls are fun and blocks are really really fun. And anything that is nesting - we have a set of nesting blocks she loves to put in each other.
If you're looking to spend more $$ - a push-trike type of thing is really neat. My dad made one for Nora for her first birthday and she was a big small for it - but plays with it all the time now that she's 16 months.
"(her godparents - who don't have kids yet got her the 96 count of crayolas - yikes!):"
I actually have a baby now but a few years ago when I didn't I went to a party for one of my best friends kids. The baby was turning one. What did I get her? An inflatable table you could write on with MARKERS. My friend looked at me like she was going to throw me out the window. I was just like "what??? Its cool right!?" HA! Now that I have a son I know better!
DD really got into baby dolls around her first birthday. She really likes the ones that come with bottles and other accessories. Goodnight Gorilla was her favorite book back then, and was for quite a while as well. Finally, washable markers were something she enjoyed.
My best friend's baby just turned 1 and we went to the party last weekend. Right now the biggest hits with her are stuffed animals (which I know makes a lot of parents cringe) - the bigger the better. She really loves pooh and eeyore; she already had a large eeyore, but she got a large pooh and I think that was her favorite gift since she can drag 1 in each hand now.
Second, her favorite gift was books. She *loves* books more than anything I think, but I'm not sure that's typical. Plus it's hard to get her new ones, and she doesn't want to give up one she already has (if she opens it) b/c she loves to have 2 of everything!
She is getting more in to her 'babies', but her cousin who is 1 month older *hates* 'babies', so I think that isn't as much of a given as it seems like it would be. Like someone else said, I would ask first.
I would probably go with something by Little People, though. She got I think a treehouse (?) and something else and she liked both of those. She already had the ark, and she really likes the people and animals.