I had 14 stitches in my face from a cat attack when I was 5 years old... the cuts were very jagged and down to the bone, and across my whole face/cheek area. Fortunately, a plastic surgeon was on duty at the ER that day.
My scars are very, very minimal... really. People don't realize they are there unless I point them out or I don't wear make-up and even then they don't notice. And really, the one scar on my cheek that is a little bigger, I actually think it's kind of cute and would feel naked without it!
My scratches compared to your daughter's would make me think she would not have a scar... and if she did.. it would be very faint and barely noticeable.
(update)
I'm thinking the scars were more evident (puffy/red) for about a year or so after the event.
I know there are scar creams you can use in the meantime, but not sure how well they work. I know the younger the scar is, the better they work. I've heard good things about Mederma.
Here's a pic of me..
http://littlelovables.blogspot.com/2011/03/personal-style...
I have about 5 scars showing on this side of my face and no concealer on them.. The largest one is one my cheek, horizontal about an inch long closest to the bottom of my nose. They have looked like that ever since I was a kid.. no redness while growing up.