I use bed pillows for dog beds.. of course covered in corduroy because I swear my dog loves the feel of corduroy. It's also cheaper than buying a box of fluff. I know a bed pillow would not fit inside that pattern but you could measure the pillow and figure out the square size to cover the pillow just like in the picture. It's just a simple square. The only difference is that the pillow would probably hold up better in the wash than just fluff. It's the cost of the fluff that would cost a lot. This pattern calls for 6-8 16 oz bags of fluff. I know a 5 lb box of fluff costs about $40 without a coupon. I go through a lot of fluff in my job (crochet doll designer)
Just something to think about
You could also do it so that the bottom of the pet bed is zippered so you could get the pillow out for more frequent laundering