Fleece is an appropriate batting only for quilts that need to be ultra-warm (e.g., quilts for dialysis patients during treatment, very old people who struggle to feel warm, homeless folk sleeping outdoors). Thankfully your 3-year-old doesn't fall into any of these categories. The advice you've already received is sound. Stick with cotton or polyester (or a poly/cotton blend) batting or flannel for the best result.