I just looked at the pattern closely. You did not copy it quite all the way which explains your frustration:
It does not say rows 1-4 k1 p1, but what it does say is:
Rows 1-4: *K1P1* ribbing
the key part is the "ribbing"
She does want you to create ribbing and therefore for this section the knits get knit and the purls get purled. No seed stitch or anything fancy. Start with a row of k1 p1 - ending on the k1 since you have an odd number of stitches.
Then turn your work and do p1 k1 all the way back. Therefore you create the ribbing.
No moss stitch / seed stitch involved.
Then it will also look just like the picture.
I hope I could help to clarify.