I decided to basically wrap the pillow overlapping the top of the fabric about 4". I also pulled the end fabric to the seam and added another 4" on each end then cut the fabric.
When I posted the finished project the other day Pearl had not tried out her new beds. She now has and she is a very happy girl!
I am not a very good tutorialist (is that a word? spell check says no) but hope you get the idea of what I did. I'll be happy to clarify anything that is needed. If you make one please let me know, I'd love to see what fabric you chose.