If a youth size .243 is the easiest gun to grab and the kid has a few deer under her belt, I'd hand the rifle off too. I'm not going to be as familiar with that gun as her, and it might well not shoot to point of aim for me since the stock would be way too small which would throw off the aim.
On top of that, if she still has a tag, and I've used mine, letting her shoot saves a *expletive deleted*it ton of potential grief from DFW. In the end it would be OK, but for a while you couldn't be absolutley certain of that.