Quilters: help with a child's square

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Megan (4) is supposed to make a square for a class quilt.  It was suggested to me by another mom that she cut out shapes in fabric and then I sew them on. And then she could decorate the rest with fabric markers.  I was thinking of letting her try to sew on a button too and/or just picking out buttons and locations for me to sew.

But I'm not all that excited about this.  Is there something else I could do that maybe would involve her more? (and maybe be easier?)  I have no idea what I'm doing so I could be missing some really easy solution here!

Also for the sewing what kind of stitch do I need to do?  I don't have a sewing machine and I probably haven't sewed since HS... so I'm hoping just a simple stitch (I don't even know stitch names) will work?

Any tips, thoughts, ideas are much appreciated!

Thank you!