I am with everyone else about not using a batting and now that I have read that you only have a small area that _might_ show through, I would go for it without batting. I suggest that a fluffy blanket that is not too heavy will be loved and used much more than one that may be too hot or just plain too heavy for a little one. Good luck, and please post a picture of the completed quilt. I know I would love to see it.

fleece backed quilts are Wonderful!
you can choose a really lightweight batt, or a layer of flannel, or (for one quilt i did that had show-through) i used a layer of muslin instead of batting-it worked well....i would not use 2 layers of fleece- but i often use fleece for backs & i pretty much always either use a batt or a layer of muslin or flannel....works great.
as for direction- pull on the fleece in both directions- one direction will stretch more than the other- i generally load so the stretchiest is (side to side) with least stretch lengthwise. then just make sure you (smooth) as you go- don't stretch- makes fabulous baby/kid quilts!!!