A. - 3 year olds can learn so much about their Savior in Sunday School! It's a great time to teach them the Bible stories as well as how to sit nicely in church.
In our congregation, Redemption Lutheran in Lynnwood, 3 years old is the beginning age of our preschool class. They learn a short Bible story in language they can understand, usually using felt boards or cut outs on popsicle sticks as the characters so they can attach the visual story to the verbal one. Then they do an activity or coloring which reinforces the lesson. Singing is also a large part of the class, because preschoolers retain so much from song.
Don't be afraid to ask to stay the first couple times to see what they do. Hang out in the background so that your daughter can be a "big girl" and not need you there, but it's important to know that there is an opportunity to learn about God, and not just babysitting time.
Blessings to you!