This is the kind of quilts I make with kids; I've done it at synagogue 'mitzvah days,' most recently, with my daughter's Girl Scout troop. It's a great way to use up novelty and conversational prints!
I had the girls organize themselves into 3 2-4 member teams, and gave each team a large piece of flannel to serve as their design wall (big enough to hold all the squares - a 5 x 5 grid for a nice sized baby quilt).
I talked to them a little about different ways to organize their blocks: contrasting lights with darks, putting similar "themed" fabrics together (put the cats in one row, dogs in another, etc.) Or just do what you enjoy.
I had the girls arrange the squares however they chose on their piece of flannels.
I had three sewing machines set up and ready for each team.
Once their quilts were arranged on their large flannel, I taught the kids chain piecing: How to flip verticle row 2 on top of vertical row 1, and stitch down the raw edge, without cutting the thread between blocks. Same for flipping vertical row 3 onto vertical row 2, etc.
This kind of chain piecing is the main thing I learned from my very first quilt book, Eleanor Burns' now out-of-print 'Amish Quilt in a Day', and it never ceases to strike me as miraculous.
Once the tops are done, I show them how to make a sandwich: Batting on bottom, quilt backing fabric good side up on the batting, and finally, quilt front, good side down, against the backing. Pin all the way around, then stitch most of the way around, (ideally, with a walking foot), leaving at 10" hole for turning.
Finally, they "birth" the quilts by turning them good side out. Stitch up the hole by machine, and then they make ties at regular intervals with colorful embroidery thread.
You wind up with a colorful, fascinating quilt that gives the makers a tremendous sense of accomplishment, and is sure to stimulate and delight any child!