Such a cute quilt. Your little girl will love it. I would suggest just stitching around pieces with a zig zag or buttonhole stitch. Using a tight zig zag I would think will distort the fabric and take away from all the cute fabrics you have collected.
Maybe use white thread or use colors if you have the time to keep changing colors. I would not use any type of clear thread for a young childs quilt. You may have problems with threads poking up.
Also make sure you use some type of stabilizer. I don't think I would use coffee filters because you want the quilt to hold up for a long time. This is probably be the one she will drag around with her all the time.
Good luck. Let us see the finished product.