We actually printed on DS's first b-day invitations "no gifts please". Of course, everyone still brought gifts, but most were very small & inexpensive (books, a kids cloth book photo album, chubby cars/trucks, other stuff I don't remember!)
Books are always a good choice. I bought several board books that I could actually read to DS at that age vs. ones without much text (a couple that come to mind that have more text than most board books are "Mama, Do You Love Me?", "Heartprints", "Big Red Barn").
DS also really started to like puzzles at that age - the one's with the large wooden knobs are easier for 1-year olds to hold.
My niece loved (and still plays with nearly a year later) the Four-in-one toy
I got her for her 1st b-day (I'm sure other places sell it too - it's called the "Four-in-One Walker" from Taf Toys by Edushape.
Another 1st b-day present I have given is growth charts. I think the one's from eeBoo
are a lot of fun, but there are tons of choices out there.
For DS's 1st b-day we asked for a Radio Flyer wagon (which he loves - it was from a family member who wanted to spend a lot of money!).
And if you get anything that's not appropriate or that you don't like (or both), you can always donate it to a shelter or the Goodwill!
Happy birthday to your daughter!
SAHM to a spectacular little boy, born 5/2003 :bf
"When you teach your son, you teach your son's son." ~ The Talmud