need some more info from ya, what is the length, the thickness you say at 1/4 or 3/16 would not work if the bow was 30" long but maybe at 48" long it would be good. also the width, i have not made any kids bows from red oak, but i would go no less than 1" wide to mid limb and then taper to 3/8" nocks. i think i would back the bow just for safety for a kid. i would probably use rawhide, burlap or some silk (found in lots of women's pants at thrift stores, make sure its 100% pure silk, the tag will say inside) for sealing the bow, polyurethane or true oil will work fine. I saw one posted somewhere where a guy made one for his daughter that was pink painted and then sealed. very nice for a little girl, i know my little one would love a pink bow.
just my .02 worth, hope it helps