Unless you have materials laying around you might find that making one yourself, by time you buy the component parts no cheaper....but just in case you do here is how I'd do it.....roughly...
1) make yourself a paper pattern for the base and measure the sides circumference and depths. give yourself a good seam allowance..add an extra few inches to the depth to use for folding over the pet bed rim.
2) from sturdy fabric (any strong fabric should do, old fleece blankets would be good.) cut 2 base shapes, leaving a good seam allowance.
3) if desired cut 1-3 thick layer(s) of dacron type wadding also to shape, this will give you loftiness.
4) cut 2 side shapes (again using something fleecy or otherwise strong fabric, withstanding dog claws is the aim here really)
5) right sides together sew around the outer(longer) edge of your sides.. about 1/2" from the edge. TURN RIGHT SIDES OUT before sewing a second line of stitching to take strong elastic that will later help secure your bed lining in place. (that extra 3" turn over if you left it, should now contain a length of elastic in a narrow pocket. secure the elastic in place by turning in a seam allowance and over sewing.
6) Sew one more line parallel to the upper edge to secure your turn over.
7) at right angles to your sewn lines sew again towards the bottom edge of your fabric, effectively you are making pockets that you can then stuff with wadding or other fluffy stuff of your choosing.
Once the pockets are stuffed, (you may want to do these one at a time and sew to close one by one.) manhandle the length to your sewing machine.
9) Tack your dacron fluffiness to one layer of base fabric.
10) having decided which side of your back panel is the outer side place base and dacron tacked and back panel inner side to right side..IE you want to have the dacron showing on top. sew leaving a generous seam allowance and then snip towards sewn line to ease your curve.
11) by now you have a large bundle and things are going to get tricky as you are going to feel in danger of sewing your nice fat pockets into the middle of the base.
12) as if capturing the pockets/ side piece, ease it on top of the dacron and sew inside the previous seam ..you should end up with a big base shaped pocket that you can then turn the right way out and finish by over sewing the opening. for extra strength adding a contrasting fabric as a binding edge would be nice.
If in doubt do it all in paper first
hope that sort of made sense.
If really really in doubt save yourself the hassle and buy one