You might just use a piece of fleece for the "batting". And I would either just use the quilt backing to finish it or double-fold bias tape.
DD has a little doll quilt we made her a few weeks ago. She wanted her own project so I had her cut up fabric into pieces, and made a 12" crazy-quilt square out of the pieces. It's really cute! (Since she's just 4, she obviously didn't do any of the sewing.

)