if this quilt is a comfort quilt for a baby or a wrap-around for tv watching, why put on a backing? i've made those kinds of quilts without a backing and they have been as cozy as can be. the batting will not shrink, especially after washing and drying. make sure to use a fabric softener sheet or liquid because there will be a lot of static cling. if you don't use the best quality fleece it will pill after several washings but it would do that inside a sandwich too and you would feel the little bumps. i have one of those tiny mustache trimmers and i shave the fleece pilly-things off every now and then. mine doesn't have to last forever. i tied one for tv watching. yum! by the way, that stuff is colorfast so if the top is also, then it will withstand baby formula and other baby stuff, if you know what i mean.
but if you plan to put a lot of work into the project then use true batting and backing. don't let good work be ruined by materials not made for the job.