Discouraging beaver behavior

Our daughter gnaws on the crib railing and I'm afraid this project is too little; too late since most of the paint, and even some of the wood, has been chewed away. 

I realize there are probably fancier ways to do this out there, but I went for quick and easy. First I took an old crib sheet and sewed a long hallow tube. I stuffed it full of batting and sewed up the edges. Then, I glued it right there on top of the crib rail. Yep. Just glued it. Damage was already done so why not? Next, I hemmed a long rectangle and draped it over the top of that fluffy tube. I sewed buttons to hold it in place and voila! At least our little girl won't be eating any more paint, or wood... from the front railing. I wonder if she'll find a new rail to chew, or if she'll end up with a mouth full of stuffing...