Kids? Doing service? You bet. No child is too little to help others.
In addition to teaching about Jesus’ example of service, you may want to help them apply it, real time. Talk about how Jesus helped others, then add an actual pint-sized service project to your Sharing Time lesson, to help children to serve as Jesus served. Think about someone in need in your ward or community: perhaps a homebound ward member, a sick child, local nursing home residents, hospitalized children, missionaries serving in your ward, missionaries serving elsewhere who grew up in your ward, etc.
A child can draw them a picture or make a card to cheer them up. Older children can write letters about what they’re learning in Primary. You can make this simple (paper and crayons/pens) or elaborate (stickers, markers, buttons, lace).