Hi Eileen -
If you want something TOTALLY easy, try this one I did last year for my four year old daughter, who loved the soft, fuzziness of the yarn and the light purple color.
I used Lion Brand Velvet Spun yarn in lavender color. I liked this yarn as a beginner because it doesn't split. I think I used size 9 needles, and cast on 9 stitches (you can go more or less for a wider/thinner scarf, just be sure it's an odd number of stitches cast on.)
Then K1, P1 to the end of the row.
Next row, also do K1, P1.
Continue until the scarf is about45 inches long (or however long your daughter wants it to be). This scarf, like most of the others I've done now, will stretch with wear.
This is the seed stitch, which lies flat, and to my beginner eye looks like it's more complicated than it really is, and better than garter stitch (K only).
The only caution I'd have is don't try to put a fringe on the ends of the scarf because the yarn unravels and sheds.
Hm, this is my first post. I'll try uploading a photo.