This could be done with toddlers or preschoolers too, with just an augmentation of the actions.
Five Little Monkeys Jumping on the Bed
Everyone should be familiar with this song. There is a picture book and board book of the song, as well as a million iterations on youtube with various characters taking the staring roll of the monkeys. My two year old is OBSESSED. If you ask her what the doctor says if you jump on the bed, she'll tell you, "Fall off bump head!"
So while I will fully admit that this song is annoying, its a big hit with the toddler set.
The Wheels on the Bus
Another familiar song. But again, mega hit with the toddler set. A fun idea is to ask the kids at your storytime what their favorite animals are and what sounds they make. And then put them on the bus too! They will love the element of surprise with cows on the bus going moo, moo, moo and other animals. You can also include gross motor skills, like "the monkeys on the bus swing back and forth." This is a great way to bring familiarity to the song, even if they children have never been on or seen a bus.
The muscles children use for tearing paper are the same muscles they use for writing. Every time you do an activity that exercises these muscles, you are helping your little one get ready to write!
After Story Activities
Mail Time Matching Game This activity requires envelopes (at least one per child) and four small cardboard boxes. You could also use mailboxes, if you have access to those. Ahead of time, draw a large shape (circle, square, triangle, or diamond) on each box. Draw one of the shapes on each envelope. If you like, cut slits in the boxes (large enough to easily accommodate the envelopes). During storytime, hand out an envelope to each child and encourage children to find the matching boxes to deliver their mail. If you like, provide paper and crayons so that children can draw or write letters or pictures, fold them and place them in their envelopes, and "mail" them.
This activity is suggested for preschoolers, but my toddler loves to collect the mail and I can imagine she would fine this fun too! This would be a great in a dramatic play area as well.
Dramatic Play Area
Set out community helper hats and props for children to interact with. Or create a post office, doctor's office, vet clinic, dentist's office, etc.