When mounting on the wall, I would suggest raising it higher than your dog. That way you don't end up with dog fur on the bottom of the design wall, from your dog brushing up against it.
I have styrofoam insulation boards, which I really like, covered with batting. My problem is we have cats who absolutely LOVE to shred styrofoam and batting. I can't leave it up.
Edit: I found that large blocks, and sewed rows of blocks, do not like to adhere by themselves even with the design wall tilted. Smaller blocks do not have this problem. Anyway, I like the styrofoam because I can pin into it. I would recommend bringing some pins with you when buying the backing board to make sure you can easily pin into it.