I would be very upset if someone used one of my quilts for a doggie bed, at least while it was new and beautiful. What happens to it when it's old and worn out --- well, I'll be dead by then, so I won't care.
My policy is to never, ever give a quilt to someone who hasn't asked me for one. I assume if they ask, they are interested in having a quilt. There are just too many people out there (my relatives included) who don't have a clue as to how much work, time and money goes into a quilt. Sometimes you have to ask what kind of quilt they want as well. My niece used to think quilts were "horribly old fashioned" until she saw a blue jeans quilt and asked me to make her one. She adores it! Has her whole bedroom done in denim now! One sister never was one for quilts, until she saw one in a catalog she adored, and sent me the photo. To me, it was boring to make: all big blocks, but great colors. I couldn't have made her happier if I'd sent her pure gold! So, as a caveat, make sure the person wants a quilt, and make sure you give them the quilt they want. And if they don't seem to want a quilt, for Pete's sake, don't give them one!