They will be fine keep an eye on her though she may be sick the reason they usually start pecking on another chick in the group is because they see something different in her.
Pullet-girl chicken from hatch until a couple months into laying
hen - girl chicken that has been laying more than a couple months
cockerel- boy chicken under the age of 1
rooster- boy chicken above the age of 1
chick- a word that can be used in place of pullet or cockerel up to the age of 10 weeks