Even though we do not know your daughter's size, or experience...
I ALWAYS start a new shooter with a Semi Auto in 20 gauge. Male, Female, big or small.
Gun fit to shooter is very important! I would suggest letting her try a bunch with some qualified lady shooters to find gun fit best to HER. Rem 1100, Browing Gold, Beretta 390/391 are 3 great guns. Each fits a bit different. Ladies do better with addressing other ladies needs.
I have experience in teaching ladies - still I ask for other ladies to assist me.
Great buys in LNIB exist as well.
Now the best kept secret is 1100 in 20 ga [as the adage goes] these other two fit the bill as well.
TOO many of these "first guns" also saw double duty as HD guns. Even if down the road she gets a 12 ga, or goes to learning a pump, or she gets O/U in 28 ga ...that first gun- semi in 20 ga - is special, sentimental, will take clays, feathered critters, furry critters, critter-critters.
Gets older, and as time goes on...that semi 20 is easy to tote, easy to shoot, and will be there in old age and daddy has since passed. She can teach her kids to shoot, and pass it down...
steve