I would go with Ruth's idea...muddy paw prints on white paper...use the prints as a pattern to cut pieces to applique on your quilt square. I've seen an applique pattern somewhere that's done like that. I'll search and if I can find it I'll post it for you.

Maybe something like this would work?

O.K. Think I got it now. Muddy Paw Print on dull side of freezer paper and dry print carefully with hair dryer.

Cut out the print by making a little hole in the center of each print and cut out the whole thing - leaving the paw print intact. - like we used to do when we made valentines - remember we'd fold the paper in half and cut out the valentine - what was left was a stencil of a valentine. That's what you want to do - use the stencil. Iron it on where you want the paw print to be and then you can paint it in with acrylic paint, using a facial sponge or even your finger.. Pull off the stencil, then iron the print. Please try it out on scrap fabric first. If you are careful you can use the stencil a few times. Make sure paint is not too thin.

Wow! These are all great ideas, thanks!