I made a quick quilt that had fleece as its backing and even though it was quilted well, over time the seams started to let go. I think it was because the fleece is very flexible and doesn't really support the piecing very well without something a little more inflexible in between the layers.
I know a dozen or more people will say they had no problem with it, but I DID! If I were to ever do it again ( not likely) I'd use a piece of muslin between my piecing and the fleece. If it is a quilt that you can see being used to line the dog's kennel in a few months, go for it! If it is something that will be cherished, add the muslin!