My first thought is that you have 3 or 4 colors in the kitty backgrounds (green, blue, beige and a rusty). I would make rectangles (twice the length as the width) of each and use that as a border strip. Not sure how much bigger you want the quilt to finish, I would do this border the same width as your brown border and then bind in the brown. I just think it would be a colorful piece without being distracting and be easy to do. Please be sure and post whatever you decide (I'm sure it will be great!).

I do a lot of scrappy quilting, so I would find fabrics that match lots of the different colors in your cat blocks, then I would sew up scrappy 4 patches to go all the way around. To make it rectangular rather than square, you can add 4 patches to the sides and add an extra row or two to the top and bottom. Then I'd made a final outer border from the sashing fabric, and perhaps bind it with that too.