I know a whole slew of under-10 Graces, as well as one about 50, who also felt her name was old fashioned.
I know an 8yo Clark.
I still remember when Emily was a grandma name, and meeting my first young Emily. She was the niece of a friend, an adorable little toddler. One look at her and all of a sudden the name seemed young again. She would be about 35 now, and since then, yes the name has become hugely popular. I love your dd's name, too. Would have loved to use Adeleine or Adele for a dd but it doesn't sound good with our last name.
Other "grandma/pa" names that are very common among kids in my area are Sophia, Isabella, Emma, Hannah, Kate, Chloe, Ava, Samantha, Olivia, Abigail and Noah.
Less popular, but those I know at least one child with the name are Lydia, Violet, Ada, Ivy, Meredith, Miranda, Rose, Pearl, Claire, Stella, Audrey, Audra, Owen, Samuel, Edward, Zeke, Charles, George, Elijah and Joseph.
Names that are common in my age group but sound old fashioned to my teen and her friends are Kathy, Jennifer, Linda, Patty, Kelly, Stacy, Debby and Tammy.
Names I haven't heard on anyone under about 70 are Edna, Henrietta, Agatha, Agnes, Muriel, Kay, Dick, Harold, Lester and Fred.