I tried SITD and wasn't good at it at all. So I changed to SOutsideTD, and called it art.
Seriously, it takes practice to master it.
The quilt top is beautiful; love the fabrics and the colors.
How about using invisible thread if you don't want the wayward stitches to show? I've never used it myself so can't tell you anything about using it.
If your machine has a curvy stitch - you know like an elongated "S" on it's side - that could work for you. I don't know if you can use the walking foot for that, though.
Good luck. No matter what you do, your daughter will cherish the quilt!