If you have a needle down function on your machine, it's a life saver on machine applique. It allows you to raise the presser foot and reposition the fabric as needed. Stop with the needle down on the outside side of the circle to reposition. Have you thought about doing a simple staight stitch about 1/8 in from the eyeball edge and allowing the edge to fray like in raw edge applique. It would be easier I think. If button eyes are put on make sure they are small to not pose a choking hazard for small children.They do look very cute!